Wittgenstein

http://www.cambridge.org/0521809363

WITTGENSTEIN’S TRACTATUS

Wittgenstein once wrote, “The philosopher strives to find the liberating word,that is, the word that finally permits us to grasp what up until now hasintangibly weighed down our consciousness.” Would Wittgenstein have beenwilling to describe the Tractatus as an attempt to find “the liberating word”?The basic contention of this strikingly innovative new study of the Tractatus isthat this is precisely the case. Matthew Ostrow argues that, far from seekingto offer a new theory in logic in the tradition of Frege and Russell, Wittgen-stein from the very beginning viewed all such endeavors as the ensnarementof thought.

Providing a lucid and systematic analysis of the Tractatus, Professor Ostrowargues that Wittgenstein’s ultimate aim is to put an end to philosophy itself.The book belongs to a new school of interpretation that sees the early Witt-genstein as denying the possibility of a philosophical theory as such. It isunique, however, in two respects. First, it is the only “nonstandard” readingthat offers an extended account of the central topics of the Tractatus – thepicture theory, the notion of the variable, ethics, the different sense of analy-sis, and the general form of the proposition. Second, it highlights the intrinsicobstacles to any kind of general or summary understanding of Wittgenstein’sthought.

“ . . . an original, detailed and highly compelling interpretation of Witt-genstein’s philosophical aims and central concerns. Ostrow shares Dia-mond’s and Conant’s sense of dissatisfaction with the traditional read-ings of the work, but the interpretation he offers is significantly differentfrom theirs and represents the first book-length attempt to develop analternative approach in a systematic way which engages fully the detailsof Wittgenstein’s text.”

– Marie McGinn, University of York

Wittgenstein’s Tractatus

A Dialectical Interpretation

MATTHEW B. OSTROWB oston University

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CONTENTS

Preface page ix

Introduction 1

I Pictures and logical atomism 21

II What is analysis? 46

III The essence of the proposition 79

IV The liberating word 125

Notes 137

Bibliography 165

Index 171

ix

PREFACE

This book grew out of a larger project, an attempt to draw a philosoph-ical connection between the early Wittgenstein and Plato. While Icontinue to believe that such a connection exists and that it can beinterestingly drawn, the original study, as it stood, was too ambitious;over time, I have come to the (perhaps painfully obvious) realizationthat a serious attempt to come to terms just with Wittgenstein’s Trac-tatus is more than enough for one book. Nonetheless, what initiallymotivated the project is what, at bottom, continues to draw me toWittgenstein: the concern with the nature of philosophy itself. Indeed,I believe that for Wittgenstein – early, middle, and late – the questionof philosophy’s nature is the central question of all of philosophy.Such a contention may seem surprising. For while Wittgenstein’s

reflections on the philosophical activity, particularly those in the mid-dle of the Philosophical Investigations,1 are among his most oft-quotedclaims, we must acknowledge that these represent only a very smallportion of his total writings. Moreover, in the Tractatus, the text withwhich we shall chiefly be concerned here, the issue is almost entirelyabsent, forming the subject matter of a mere eight remarks (TLP4.111–4.116). In order to view Wittgenstein as placing such primacyon the question of philosophy, it might then seem that we would haveto give extraordinary weight to just a few passages.But this will not be our approach. Instead of seeking to privilege

the meager store of Wittgenstein’s general reflections on philosophy,we shall take as our starting point the complete set of remarks thatmake up the Tractatus. Such an approach makes it evident that Witt-genstein, as we shall read him, does not understand the question ofphilosophy’s nature to be some “meta-issue,” but, rather, one that

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pervades what one ordinarily would think of as the content of thediscipline. The traditional concerns of philosophy are, we might say,transformed by Wittgenstein into the means by which we can reflecton philosophy. It is the fundamental task of what follows to seek tobring out how this can be the case.Many people have helped me, in one way or another, with the

lengthy process of writing this book. First and foremost, I would liketo thank the late Burton Dreben. I am thankful to him as a teacher:He showed me what it is to think about philosophy at the highestlevel. I am thankful to him as the keenest of critics and collaborators:He spent many hours with me working through the nuances of myreading of the Tractatus. And I am thankful to him as a friend: Hiskindness, humor, and interest in my work were invaluable to me.Nearly every page of this study reflects his powerful influence and Iremain deeply indebted to him.Charles Griswold also played a central role in the birth and devel-

opment of this book. His subtle and imaginative reading of the Platonicdialogues provided part of the spark for the initial project. Further-more, I am deeply grateful to him for his ongoing support, advice, andencouragement.Juliet Floyd was exceedingly generous with her help and encour-

agement in nearly every phase of the writing process. Moreover, Ihave been very much influenced by her penetrating and original read-ing of Wittgenstein, and by exposure to the elegance of her philosoph-ical style. I owe her a large debt of gratitude.I would also like to thank Terence Moore and Matthew Lord of

Cambridge University Press and my Production Editor, Laura Lawrie,for their assistance and support. I am grateful as well to the EarhartFoundation for the two years of financial support during the studythat formed the indispensable background to this book.Many others have contributed to this study – perhaps at times

without even realizing it – and indeed deserve greater acknowledg-ment than I can offer here. I have had extensive and very fruitfulconversations about the Tractatus with Rosalind Carey, Denis Mc-Manus, Joe McDonald, Andrew Lugg, and Anat Biletzki, and aboutphilosophy more generally with Bruce Fraser, Thomas Woodard,Lawrence Pasternack, Phil Cafaro, Klaus Brinkmann, David Roochnik,and my brothers, Michael and Daniel Ostrow. Victor Kestenbaum tookan interest in my work and offered his advice and encouragement at

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a time when these were sorely needed. David Stern provided veryhelpful comments on an earlier draft.I have also had enumerable philosophical conversations with my

wife, Theresa Reed. For that alone she would deserve my amplethanks, but, happily, her involvement with this study has extendedfar beyond that capacity, far beyond, in truth, what I can begin toexpress. Suffice it to say that this book would in no way have beenpossible without her.Finally, I would like to thank my father, Seymour Ostrow, and my

late mother, Judith Alling, who I dearly wish were still here to discussit with me.

1

INTRODUCTION

I

Wittgenstein, in conversation with Moritz Schlick, once characterizedhis fundamental goal in philosophy as follows: “Everything we doconsists in trying to find the liberating word (erloesende Wort)” (VC 77).Similarly, we find in The Big Typescript: “The philosopher strives tofind the liberating word, that is, the word that finally permits us tograsp what up until now has intangibly weighed down our conscious-ness” (PO 165).1 Both remarks were made in the 1930s, years afterthe publication of the Tractatus: with their depiction of philosophy asthe pathway out of psychic encumbrance, they quite naturally call tomind Wittgenstein’s later, explicitly “therapeutic” thought (cf., e.g., PI133). But, we might ask, could such claims be applied to Wittgenstein’searly work as well? Would Wittgenstein have been willing to describethe Tractatus itself as an effort to find “the liberating word”? My fun-damental contention in this book is that this is indeed the case, that,far from seeking to offer a new theory of logic, to continue the philo-sophical legacies of Frege and Russell, Wittgenstein from the startviews all such endeavors as the ensnarement of thought. The Tractatus,I shall aim to show, is nothing but an attempt to set down in definitivefashion the way of release.For those involved in writing and reflecting on early analytic phi-

losophy, such an assertion is likely at once to locate this study in thegrid of a familiar set of dichotomies. It would seem to herald a non-metaphysical interpretation of the Tractatus as opposed to a standard,metaphysical reading, an emphasis on the continuity of Wittgenstein’sthought rather than the notion of a radical break from an earlier,

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more traditional philosophical stance, an insistence on the nonsensi-cality of the text’s propositions as against the possibility that theymight manage to communicate a kind of indirect truth.2 And, in avery broad sense, those expectations will be met by what follows. Butwhat animates this book is the belief that that “sense” is entirely toobroad – that is, that the terms in which these standard oppositions areformulated are simply not adequate to the Tractatus. Do we reallyknow in general just what it means for a proposition or set of propo-sitions to be “metaphysical” rather than “nonmetaphysical”? Is thefundamental aim of a philosopher’s thought so open to view that wecan at once recognize when a given piece of writing does or does notcohere with it? Do we understand the claim that a work of philosophyis simply “nonsense”? It is not, of course, that Wittgenstein leaves uscompletely unequipped for such questions; on the contrary, I wouldsuggest that, in one form or another, they lie at the heart of theTractatus. But just this fact renders notions like “metaphysical,” “non-sense,” and so forth ill-suited to any sort of explanatory task in thiscontext. They are, we might say, too much part of the problem toconstitute a potential solution.One might then imagine that what will here be proposed is an

alternative vocabulary in terms of which our interpretation is to beconducted – our own set of privileged categories. But I shall argueshortly against any such strategy. Instead, what we must acknowledgeat the start is just the problem that is posed by the attempt to interpretthe Tractatus. If we grant that Wittgenstein’s aim here is, in one wayor another, to call into question the traditional language of philoso-phy, we must realize that this is not just the language of Frege, Russell,Moore, et al., but also our language: precisely the depth and compre-hensiveness of this text’s critique of philosophy deprives us of our, asit were, clinical distance as commentators on the text. What we find,I believe inevitably, is that we cannot insulate ourselves from thedifficulties with which Wittgenstein is concerned, that the philosophi-cal commitments that are revealed in our own manner of textualanalysis are the very subject matter of the Tractatus. The Tractatus seeksto expose the extraordinary confusions inherent in the process ofphilosophical inquiry. To understand and write about that text, wemust be willing to allow that these might be our confusions as well.

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II

In order to get a preliminary view of the difficulties that we mustconfront, let us then return to the remark with which we began. Whatdoes it really mean to read the Tractatus in terms of a fundamentalconcern to “liberate” us from philosophical confusion? One might wellgrant something of this sort as the young Wittgenstein’s aim; he does,after all, already in the Preface portray his book as intending to showthat “the problems of philosophy” rest on “the misunderstanding ofthe logic of our language” (TLP, p. 27).3 Nonetheless, one could quitenaturally construe the basic form of the Tractarian critique, if not itsdetails, in traditional philosophical terms, as an attempt to provide arefutation of the misunderstandings and errors of the past. On thisreading, Wittgenstein proclaims various philosophical positions to be“nonsense” (see, e.g., TLP 4.003, 5.5351, 6.51) in the way that somany philosophers in the Western tradition have dismissed their pred-ecessors’ claims – namely, as being patently false or absurd. Such aview has in fact been implicit in much of the literature on the Tractatus,beginning with Ramsey’s review4 and the responses of the Viennapositivists, and continuing with the work of more contemporary com-mentators like Black,5 Stenius,6 Hintikka,7 Hacker,8 and Pears.9 Char-acteristic of this approach – which would include a quite diverse set ofinterpretations – is the insistence on treating the Wittgensteinian at-tack as if it presented, in opposition to the tradition, a series ofstraightforward philosophical accounts: accounts of the proposition(the “picture theory”), the tautologous nature of logical truth, theineffability of logical form, and so forth. These accounts are thencriticized or modified by commentators in accordance with the de-mands that are presumably to be satisfied by a well-constructed phil-osophical theory.One rather large obstacle to this approach to the Tractatus is repre-

sented by remark 6.54. Here Wittgenstein famously declares: “Mypropositions are elucidatory in this way: he who understands mefinally recognizes them as nonsensical (unsinnig), when he has climbedout through them, on them, over them.” If we take this remark seri-ously, it would appear difficult to treat its author as someone who hasintended to present a straightforward theory, a series of claims to beevaluated in terms of their truth value. Still, the responses on the partof Tractarian commentators to this move have been varied. Perhaps

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most commonly the tendency has been to disregard this remark, or toignore its consequences with respect to our understanding of theseemingly substantive details of the text. For such readers, this remarkis regarded as striking, but not as a central feature to be accommodatedwithin a satisfactory interpretation.10

A second type of response involves an attempt at softening theimpact of the text’s harsh self-assessment. One notable example of thelatter strategy is Carnap’s interpretation of the statements of the Trac-tatus as purely linguistic proposals.11 For Carnap, while philosophicalpropositions of the sort espoused by Wittgenstein (and the Viennapositivists) make no claims about the world and thus are not true orfalse, they are not like many traditional metaphysical assertions inbeing entirely nonsensical. Instead, legitimate philosophy is to be un-derstood as consisting of elucidations, purely formal assertions thatserve to clarify the logical syntax of the language of science. In thissense, they can be seen as having the empty character that Wittgen-stein ascribes to the tautologous propositions of logic.12

A second example of an explicit attempt at moderating the Tracta-tus’ view of its own utterances is found in commentators like An-scombe,13 Geach,14 Hintikka,15 and Hacker.16 The strategy they employis motivated by remarks such as TLP 5.62 (“In fact, what solipsismmeans is quite correct, only it cannot be said, but shows itself.”), 4.115(“[Philosophy] will mean the unspeakable by clearly displaying thespeakable.”) and 4.1211 (“Thus a proposition ‘fa’ shows that in itssense the object a occurs, two propositions ‘fa’ and ‘ga’ that they areboth about the same object.”). In these remarks and elsewhere, Witt-genstein seems to suggest that, while the attempt to state what isproperly to be shown results in what he calls “nonsense,” somethingintelligible is nonetheless thereby expressed. We are then led to sup-pose that Wittgenstein’s propositions – if not the propositions of allmetaphysics – are nonsense only in a special sense. To be sure, so suchcommentators continue, they are not strictly utterable, according tothe standards of significance established by the Tractatus. Still, theysomehow manage to convey to us important philosophical truths: atthe end of the book we “know” that, in reality, the world is composedof facts, not things, that a common logical form binds together lan-guage and the world, that value lies outside of the world, and so on.Except, of course, we cannot actually say these things, but must onlythink them, silently to ourselves; or perhaps we may repeat them –

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grudgingly – to another, but always with the acknowledgment that inso doing we have transgressed the strictly proper bounds of sense.More recently, Cora Diamond, beginning with her important paper

“Throwing Away the Ladder,” has presented a central challenge to thisreading – and, indirectly, to the related interpretation offered by Car-nap.17 Diamond, in effect, attributes to Wittgenstein the position ofRamsey in his oft-quoted criticism of the Tractatus’ notion of showing:“But what we can’t say, we can’t say and we can’t whistle it either.”18

That is, refusing to countenance the possibility of any sort of meaning-ful gesture toward the ineffable, she bites the bullet on Wittgenstein’sbehalf and proclaims that, as far as the Tractatus is concerned, its ownstatements really are nonsense, plain and simple. There is no Tractar-ian counterpart to the Kantian Ding an sich, no deep features of realitythat are somehow made manifest in Wittgenstein’s utterances. Instead,we must take Wittgenstein at his word at 6.54 and realize that, in theend, all the pronouncements of his text are just so much gibberish.Now I have a good deal of sympathy with – and have been much

influenced by – Diamond’s approach, and the elaboration of it pro-vided by James Conant. Nonetheless, I think one must take care to beas clear as possible about what this position really comes to, as it caneasily serve to mislead. Given the importance of the Conant/Diamondinterpretation in framing the contemporary debate about the Tractatus,I want then to consider it in some detail (my focus will be on Dia-mond’s initial paper).To begin with, Diamond suggests that Wittgenstein’s conception of

nonsense and his concomitant show/say distinction have their rootsin Frege’s so-called concept “horse” problem. Frege, in the article“Concept and Object,” dismisses as incoherent Benno Kerry’s conten-tion that there can be concepts – like the concept “horse” – which alsocan function as objects. For Frege, the concept/object distinction ismutually exclusive: a concept by its very nature is predicative or, ashe also puts it, “unsaturated”; conversely, the object, as a logical sub-ject, serves necessarily to fill the gap left by the concept. In Kerry’sexample, then – “the concept ‘horse’ is a concept easily attained” – thefirst three words do not designate a Fregean concept, but, as is indi-cated by the appearance there of the definite article, a Fregean object.The peculiarity of having to maintain that the concept “horse” is not aconcept is dismissed by Frege as an “awkwardness of language” (CP185) and, moreover, as Diamond reads him, one he believes will not

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be encountered in a logically perfect notation like his Begriffsschrift.Thus, in the Begriffsschrift, statements about concepts and objects ofthe sort represented by Kerry’s example – indeed, the very claim thatthere is a fundamental distinction between concepts (or functions)and objects – will not be formulatable. Instead, that there is such adivision will come out in the distinctive use of the signs of the nota-tion.Diamond then terms remarks like the one expressing the difference

between concepts and objects “transitional”;19 their purpose is solelyto lead us into the Begriffsschrift, to begin operating within its para-meters. But once we have effected this transition, these remarks arerecognized as completely without sense and are in fact inexpressible.Here we begin to see how Diamond draws the connection with Witt-genstein. For her, Wittgenstein is fundamentally concerned to extendto the whole philosophical vocabulary Frege’s way of excluding no-tions like “function” and “concept.” Toward that end, he is understoodas having formulated a number of transitional statements – namelyremarks 1–6.522 of the Tractatus. All these claims, as transitional, willthen have to be given up by the close of the Tractatus. After we haveread – and understood – the text, we cannot suppose ourselves to beleft hinting at some important truth with a statement like “The worldis the totality of facts, not things,” any more than we would supposethis about an attempt to state something about functions and objectsfrom within the Begriffsschrift. Instead, 1.1, like every other remarkof the Tractatus, is now seen as it really is – that is, as a claim com-pletely on par with “Socrates is frabble”20 or “ ’Twas brillig, and theslithy toves did gyre and gimble in the wabe.”21 To attempt to ascribeany further content to Wittgenstein’s claims is, for her, to “chickenout.”A quite natural first response to this approach focuses on the ex-

traordinary expressive power it attributes to the supposed gibberish ofthe Tractatus. For clearly it is not at once obvious that this text’s prop-ositions are utter nonsense, any more than it is obvious that thetraditional claims of metaphysics have such a character. If it wereobvious, if the Tractatus, Russell’s Principles of Mathematics, Aristotle’sMetaphysics, and so forth were plainly indistinguishable from LewisCarroll’s “Jabberwocky,” none of these works could ever have thepower to mislead. (Why haven’t any books been written claiming tohave established the nonsensicality of the Carroll poem?) Wittgen-

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stein’s claims are then assumed to be capable of themselves effecting the“transition” Diamond describes, of somehow bringing us to recognizethe fact that they are, contrary to all appearances, absolutely devoidof sense. Indeed, in “What Nonsense Might Be,”22 Diamond sketchesin some detail Wittgenstein’s account of the precise way in whichphilosophical nonsense is to be viewed, suggesting, in particular, thathe rejects (what Diamond takes to be) Carnap’s view that it consists ofcategory errors.23 But this is as much as to acknowledge the specialcharacter of the Tractarian propositions, their dissimilarity to pseudo-sentences like “Socrates is frabble.”24 The latter expression, after all,would seem to have none of the capacity for self-illumination that isthought to belong to the remarks of the Tractatus. We might say that it“shows us” that it does not make sense, but this is a result of ourunderstanding the syntax of the English language; if we did not al-ready know that syntax and were not therefore at once inclined tocall the expression “meaningless,” it surely could not itself teach usthat (let alone why) this is the case. The point, in short, is that themore that Witttgenstein’s claims are assimilated to ordinary nonsensesentences, the less easy it becomes to explain the possibility of ourever coming to recognize them as such.Diamond, however, might seem to have developed a response to

this sort of objection, one which she elaborates in a more recentarticle, “Ethics, Imagination, and the Method of Wittgenstein’s Tracta-tus.”25 Central to this part of her account is Wittgenstein’s emphasis in6.54 on himself as subject. For, she points out, this remark does notproclaim that he who understands my propositions “finally recognizesthem as nonsensical,” but rather that he who understands me so rec-ognizes them.26 This distinction between understanding the utterer ofnonsense and understanding the nonsense itself is, for Diamond, cru-cial. For while the Tractatus’ remarks, as devoid of sense, are incapableof being understood in themselves, we can still attempt to understanda person who would wish to proclaim such empty strings. This involves“a kind of imaginative activity, an exercise of the capacity to enter intothe taking of nonsense for sense, of the capacity to share imaginativelythe inclination to think that one is thinking something in it.”27 On thisreading, the Tractatus is then seen as an attempt to, as it were, conjureup the state of mind of someone who has an inclination towardmetaphysics. It does this, however, always with a therapeutic intent –that is, with the aim of helping the individual explode the illusion that

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fosters his metaphysical tendency. Diamond in this way believes shecan account for the illuminating potential of the Tractarian remarks,locating this not in those remarks’ “internal features,” but rather inexternal features of their use;28 what allows Wittgenstein’s nonsensicalutterances to be liberating is just their utterer’s recognition of them asnonsense.But while this account is suggestive and interesting, one still worries

about its tendency to inflate the Tractatus’ notion of nonsense, evenwhile insisting on its ordinariness. What is it about Wittgenstein’ssupposed babbling that could so stimulate our imaginations, and directthem in such a particular manner? Or, alternatively, one might won-der whether we can really make sense of Diamond’s notion of the“imagination” (a term, after all, that does not play much of a role inthe Tractatus). One wonders how imagination could bring us to “un-derstand” a person, if all we have at our disposal are his absolutelyunintelligible strings of words.29

How would Diamond reply to these objections? I suspect she wouldview them as placing a kind of pressure on her interpretation that itwas not intended to bear: we could be seen here as fastening on towhat is for her only a kind of rhetorical move in a polemic against aconfused reading of the Tractatus. In other words, her assimilation ofmetaphysical claims to “plain nonsense” is a means of denying thecoherence of the notion of an ineffable content, but should not beviewed as saying anything more than that; Diamond’s aim is not toprovide a genuine characterization of Wittgenstein’s remarks. To de-mand from her an explanation of precisely how the plain nonsense ofthe Tractatus is illuminating could thus be said to miss the point: ratherthan seeking to provide an account of the mechanism of the text,Diamond’s purpose is simply to steer us away from supposing any rolefor its propositions – after that “mechanism” has (somehow) performedits function.We now can begin to see the real question that is opened up by

Diamond’s work, especially “Throwing Away the Ladder” and its cen-tral idea of the Tractatus as a series of “transitional remarks.” Thatquestion can be brought into full view by here asking ourselves: tran-sitional to what? I certainly agree with Cora Diamond’s premise thatmuch of the original motivation for both the show/say distinction andthe idea of “throwing away the ladder” comes from Frege’s concept“horse” problem (as well as the related difficulty inherent in Russell’s

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theory of types). But it would seem to be of paramount importanceat this point not to push the parallel too far, to realize that Wittgen-stein is shifting quite fundamentally the Fregean perspective. For letus grant for the moment that Frege has a full awareness of the impli-cations of the idea of extra-Begriffsschrift “elucidations.” Still, it mustbe acknowledged that there exists for him a concrete means of avoid-ing the utterance of such statements – namely, by always workingwithin the confines of his formal language. In other words, Frege’s(supposed) contention that certain prose judgments (the “elucida-tions”) can ultimately be transcended gains its force from the fact thatone can operate perfectly well with his Begriffsschrift without evermaking such judgments. So, for example, a statement like “There arefunctions and objects” cannot even be formulated within his “conceptscript” – “∃f & ∃x” is not a well-formed formula – but the languagenonetheless allows us to use these notions in the formalization oflogical inferences. But what is the domain in which Wittgensteinwould have us operate, once we have dispensed with the elucidationsthat constitute the Tractatus? There is, of course, a long tradition ofTractarian interpretation, going back to Russell’s Introduction to thebook (TLP, p. 8), which views Wittgenstein as concerned with layingdown conditions for an ideal language. But, while it is unquestionablethat the notion of a canonical Begriffsschrift plays an important (ifextremely unclear) role in the Tractatus, it is equally certain that Witt-genstein has not actually provided us with any such language. Wecannot confuse what are, at best, indications of some of the elementsof a proposed formalism – such as, for example, the absence of a signfor identity – with Frege’s systematic specifications in the Begriffsschriftand the Grundgesetze. The point, then, is that despite Wittgenstein’s talkof employing a symbolism that “excludes” the “errors” of traditionalphilosophy (see TLP 3.325), at the end of the Tractatus we remain verymuch within the context of our “ordinary” language, the same lan-guage in which the nonsensical propositions of metaphysics were orig-inally formulated.30

The whole idea of an adequate notation can therefore only be partof Wittgenstein’s way of leading us to a new perspective on logic, asopposed to the adoption of an actual new language. One might thendescribe the central problem that Diamond and Conant’s work pointsus toward as one of becoming clear on the nature of this perspective,once we understand that it is not embodied, as it were, in a formal

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language, in a specifiable method for eliminating the metaphysicalpseudo-sentences. How are we to characterize what the Tractatusbrings us, in the end, to see? Given the difficulties that we saw abovein the attempt to describe that insight in terms of the literal unintelli-gibility of the language of metaphysics, it may be tempting at thispoint to reach for a notion of “deep nonsense.” The propositions ofthe Tractatus really are nonsense, one will now maintain, except notin the plain, garden variety sense. They violate not ordinary syntax,but a deeper underlying structure – what the text refers to as logicalsyntax (see TLP 3.325, 3.33, 3.334, 6.124). We can then hold that it isjust toward the recognition of the claims of all metaphysics as non-sense in this special sense that the text aims to bring us.But this strategy is less promising than it may initially seem, as the

appearance of the term “logical syntax” in the above purported expo-sition of the text’s central purpose should indicate. For the necessityof here bringing in the notions of the Tractatus itself – the very notionswe have presumably “thrown away” at the book’s close – indicates thehollowness of supposing that we have, as yet, proffered any sort ofexplanation. Indeed, one now begins to wonder about the coherenceof even asking for an explanation in this context. The problem nowappears to lie not merely with how to characterize the text’s point –whether to describe it as the exposing of deep nonsense or plainnonsense – but with the very notion that we might “characterize” thatpoint at all. The difficulty, we could say, is that we are from the startassuming that the statements proclaiming the nonsensicality of theTractatus’ remarks could be true. What we are beginning to see, how-ever, is that perhaps Wittgenstein is concerned precisely to deny thepossibility of such a neutral assessment of the nature of the text’spropositions, of the nature of metaphysical claims generally. What weare beginning to see is that, for Wittgenstein, a sentence like “ ‘Theworld is everything that is the case’ is nonsense” is itself nonsense.This may seem to leave the would-be reader of the Tractatus in a

difficult, if not impossible, position. To some, the above claim willappear as a kind of reductio ad absurdum of the whole attempt to readthis text.31 Still, while I by no means wish to downplay the peculiarityof the position in which we find ourselves, I would urge that thesituation is perhaps not quite so dire. Let us then consider these threesentences:

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1. “ ‘The world is everything that is the case’ is nonsense” is non-sense.

2. “The world is everything that is the case” is nonsense.3. The world is everything that is the case.

The appearance of paradox in (1) would seem to stem from the as-sumption that the terms that compose this sentence are all used intheir ordinary senses – as if we were here committed to asserting the“plain nonsensicality” of the attempt to say anything whatsoeverabout Wittgenstein’s remarks. It is important, however, to emphasizethat the term “nonsense” must be interpreted in the same sense in itssecond occurrence in (1) as in its first occurrence within that sentence(i.e., as it occurs in (2)). That is, we understand what it means toascribe this property to attempts to characterize statements of theTractatus only to the extent that we understand the meaning of thepredicate in the text itself. But to deny, as we have, the possibility ofa general characterization of the text’s propositions is just to call intoquestion the possibility of making straightforward assertions about“the meaning” of this predicate in the Tractatus; it is to claim that anunderstanding of the term “nonsense” can only be attained throughviewing in what Wittgenstein would regard as the appropriate waythe (Tractarian) sentences to which it is appended. Precisely this pointis then expressed by (1): this sentence serves to reflect the reducibilitywithin the Tractatus of (2) to (3). The sentence (1) is therefore not itselfto be construed as somehow paradoxical, but rather as a meaningfuland – I would claim – in fact true statement about Wittgenstein’s useof the string “nonsense.”At the same time, however, we must recognize the very limited

nature of this claim; we must recognize how our capacity to makeaccurate statements about the Tractatus comes at the price of a restric-tion on their informativeness. For while the above description of therole of certain signs in this text may be correct, this description as yettells us nothing about what those signs mean – precisely what anycommentary on the text is presumably concerned to elucidate. In aninteresting way, then, the Fregean concept “horse” dilemma can beseen to extend not only to the Tractatus but also to any interpretationof the Tractatus: the commentator now finds himself in the position of,like Frege, ultimately having to ask for “a pinch of salt”; he must

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12

appeal to his reader to, as it were, jump into Wittgenstein’s text, tobegin using its language. But this, then, is as much as to admit that ourcentral question about what the Tractatus brings us to see can permitno answer. Or, better, it is to admit that whatever is proposed as ananswer cannot take the form that one will almost instinctively requireof it. For while we can offer restatements, in putatively clearer terms,of what we will claim to be Wittgenstein’s point, the force of theseconsiderations is to deprive such restatements of any privileged status,to lead us to see that they must stand on the same level as thepropositions of the Tractatus itself.It is now possible to describe in a new way Wittgenstein’s declara-

tion of the nonsensicality of his own propositions at 6.54. Rather thana neutral summing-up of the real purpose of the Tractatus, this remarkwould seem to function as a way of orienting us toward the text as awhole, of indicating how we are to read it. Nonsense, we might say,forms the lens through which all Wittgenstein’s propositions are to beviewed: we grasp his point just when we are inclined to understandthese remarks as nonsense. That, of course, is not to explain themeaning of the term “nonsense” in the Tractatus, but to face us backtoward the text. It is to suggest that the nonsensicality of Wittgen-stein’s propositions only emerges through a detailed consideration ofthose propositions themselves, that it cannot be understood apart fromsuch a consideration.32 My contention, in other words, is that theWittgensteinian view of the nature of his own claims, of philosophygenerally, is not expressible in some self-standing formula, but israther given entirely in and through the recognition of an intrinsicinstability in a particular kind of utterance; it is contained in the seeinghow our philosophical assertions change their character, how they un-dermine their own initial presentation as straightforward truthclaims.33

In different terms, what this discussion helps to make evident is thefundamentally dialectical nature of Wittgenstein’s thought in the Trac-tatus.34 It brings to the fore the extent to which we are, at everyjuncture of the book, engaged with the very metaphysics that is ap-parently being disparaged. Indeed, this dialectic can already be seen atthe very beginning of the Preface, where Wittgenstein writes: “Thisbook will perhaps only be understood by those who have themselvesalready thought the thoughts (die Gedanken) which are expressed in it– or similar thoughts” (TLP, p. 27). The appearance here of the meta-

Introduction

13

physically loaded, Fregean term Gedanke signals Wittgenstein’s intent.He is not suggesting, as it may initially seem, that only someone whohas reached the same “conclusions” as he will be able to understandthe book. Rather, the point is that these utterances have no purposeexcept for one who is genuinely tempted by the metaphysics it aims toexplode; Wittgenstein’s “elucidations” depend for their effect on aprior yearning for the deepest – and therefore, we may come to say,most empty – philosophical Gedanken.This same point is even more evident at the close of the Tractatus.

At 6.53, Wittgenstein describes the “only strictly correct method” ofdoing philosophy as an enterprise in which one would say “nothingexcept what can be said, i.e. the propositions of natural science, i.e.,something that has nothing to with philosophy; and then always,when someone else wished to say something metaphysical, [onewould] demonstrate to him that he had given no meaning to certainsigns in his propositions.” In the strict method, in contrast to themethod of the Tractatus, the metaphysical inclination of Wittgenstein’sinterlocutor is open to view. Wittgenstein will then be clearly under-stood as responding to a particular kind of utterance, rather than beinghimself gripped by an urge to spell out a series of novel philosophicalclaims. But this does not mean that Wittgenstein’s claims in this con-text are now to be regarded as obviously sensical, that his “demonstra-tion” to his interlocutor will be of a fundamentally different naturethan the “arguments” of the Tractatus. What is regarded by him as“philosophy” will thus again necessarily involve the dialectical engage-ment with metaphysics, with the urge to transcend the bounds ofsense. And that is to say once more that, insofar as we are engaged inthis process (what he at 4.112 calls “an activity,” as opposed to “atheory”), we are deprived of a neutral standpoint from which to assessits ultimate nature.

III

With the above in mind, we can begin to get a clearer sense of thenature of the “liberation” I have claimed the Tractatus aims to bringabout. Given the emphasis of so much recent literature on 6.54, onemight well suppose that this remark was in fact the text’s final state-ment, that Wittgenstein leaves us with his pronouncement of the non-sensicality of everything philosophical. In fact, though, the Tractatus

Introduction

14

ends with proposition 7’s call for silence: “Whereof one cannot speak,thereof one must be silent.” Wittgenstein’s claims, it would seem, findtheir real fulfillment not in what we say, but in what we do.But this is precisely what is required by the text’s stance, as we havecharacterized it. Wittgenstein’s final remark brings out how we are inthe end violating the spirit of the text every bit as much by proclaim-ing the complete and utter nonsensicality of metaphysics, as by pro-claiming, for example, that the number 1 is, really is, an object. Itmakes clear that the charge of “nonsense” against philosophy is not aclaim alongside the claims of science but another move in the Wittgen-steinian dialectic. That is not to deny that the move is one of particularimportance. But if that dialectic’s purpose is to be achieved, if it is tolead us to “see the world rightly” (TLP 6.54), it must ultimately cul-minate in its own cessation. Liberation, for Wittgenstein, is nothingother than the end of philosophy.It might then seem that we would best make the Tractatus’ point by

stopping our commentary right here. Of course, Wittgenstein’s owncontinued preoccupation with the problems of philosophy indicateshow difficult it can be simply to remain silent. But it is not merelypsychological compulsion that might lead us to continue – or, moreimportant, that led Wittgenstein himself to go on with philosophy. Forassuming that our aim really was to cease speaking metaphysics, whatis it exactly that we are not to say? Consider my own earlier referencesto Wittgenstein’s desire to preclude a “particular kind of utterance.”35

What kind of utterance, then? We, of course, want to say “philosoph-ical” or “metaphysical” – but do we really know in advance the exten-sion of those concepts? We are faced here with the essential difficultyof Wittgenstein’s dialectical enterprise, the dilemma inherent in theattempt to “draw a limit . . . to the expression of thoughts” (TLP, p. 27,emphasis mine). That is: we do not know beforehand exactly what isto count as an illicit, metaphysical claim; we in fact cannot know this,since to do so would be to think what the Tractatus aims to reveal asnot really thinkable.36

We could say, then, that the central task of the Tractatus is one ofsomehow delineating the class of those utterances it seeks to eviscer-ate. For the young Wittgenstein this aim is achieved by becoming clearon what he takes to be these utterances’ essence – the fundamentalimpulse that leads us to make them, the single question that he imag-ines to lie at their heart. Just this view of a unitary core to the

Introduction

15

problems of philosophy is expressed in Wittgenstein’s audacious Pref-ace claim to have found “on all essential points, the[ir] final solution”(TLP, p. 29). The same idea also appears in the Notebooks, in whichWittgenstein twice speaks of the sense that his seemingly multifariousinvestigations are all manifestations of a “single great problem” (seeNB 23 and 40). The Tractatus is then really nothing but Wittgenstein’sextended attempt to characterize that single great problem, the root ofthe drive toward metaphysics; it is a search for the liberating word.Now this whole line of thought may sound suspiciously reminiscent

of the uncharitable reading of Cora Diamond’s notion of transitionalremarks – as if I were suggesting that Wittgenstein’s remarks first makesome sort of sense and then subsequently become nonsensical. Butmy claim is that, for Wittgenstein, the revealing of the essence ofmetaphysics and the “demonstration” of the nonsensicality of meta-physics are, in fact, two sides of the same coin. To read the Tractatusdialectically, in my sense of the term, is to recognize that the successfulcharacterization of philosophy is its dismissal as Unsinn. Wittgenstein’senterprise is an attempt to lead us to a view of metaphysics so com-plete that it dissolves itself.

IV

This conception of the aim of the Tractatus both clarifies and compli-cates the task of its would-be interpreter. It is clarified, I believe, inthat we now see that we need not tie ourselves up in knots over thequestion of how the text’s nonsense can be illuminating, or of howwe can purport to explain what Wittgenstein holds can only be shown.We recognize instead that “nonsense,” “show,” “explain,” like the restof the terms of the Tractatus, have their life only within the text, thatto seek to make general, philosophically neutral claims about thesenotions is to mislead (ourselves, as well as others). Our task as com-mentators is then precisely one of describing, as accurately as possible,the role of those terms; one might say that we are engaged in an actof translation rather than one of explanation. But that is to say thatthe Tractarian commentator’s task is and must be enormously compli-cated: the successful interpretation will have the same “logical multi-plicity” (to borrow a phrase from the Tractatus) as what it expounds; itmust be as complex and multifarious as the text itself. In the Philosoph-ical Remarks, Wittgenstein writes: “Philosophy unties the knots in our

Introduction

16

thinking, which we have tangled up in an absurd way; but to do that,it must make movements that are just as complicated as the knots.Although the result of philosophy is simple, its methods for arrivingthere cannot be so” (PR 2). This remark holds for the task of Wittgen-stein’s would-be expositor as well. There is no shortcut, no simplifying,general principles that we can invoke in order to understand theTractatus – only the arduous task of working our way through its manyintricate details.In what follows, we shall involve ourselves in just such a close

textual analysis. Chapter I will discuss the opening, “ontological” re-marks (TLP 1–2.063) and their connection to the first part of thepicture theory (TLP 2.1–2.172). Chapter II will focus on the notion ofanalysis, as it is presented in the 3s and early 4s. Chapter III willinquire into Wittgenstein’s understanding of logical inference, his spe-cific response to the logic of Russell’s Principia Mathematica and Frege’sBegriffsschrift and Grundgesetze. Here we shall focus on the last part ofthe picture theory (TLP 2.174–2.225), the discussion of “sense” in the4s and 5s, and, finally, the Tractatus’ fundamental notion of the “gen-eral form of the proposition.”Our approach to the Tractatus will aim to reflect as far as possible its

author’s view of the unified nature of the inquiry that it represents.Thus, it seeks to be comprehensive, to address, at least to some extent,all the main “topics” with which this text is typically taken to beconcerned. In the interest of readability, however, this study fallssomewhat short of this ideal: in particular we shall have to ignore orgive short shrift to the Tractatus’ discussions of number, probability,scientific theory, the propositional attitudes, and of solipsism. In thefirst three cases, we can hope to justify the omissions by attempting toconvey (what I would claim is) the chief import of these discussionsthrough our account of the Tractarian notion of the sense of a propo-sition. And while I would hold that the key ideas motivating Wittgen-stein’s way of handling the propositional attitudes and solipsism willat least be familiar by the end of our study, the importance generallyaccorded to these notions would demand that, ideally, they be givenindependent treatment.There is another important issue that has been conspicuously ab-

sent from our discussion thus far. In our focus on questions concern-ing the logic of the Tractatus, we have ignored what Wittgensteindeclares, in a famous letter to von Ficker, to be the text’s real purpose

Introduction

17

– namely, the expression of an “ethical” point.37 Indeed, just such adimension is implied by our suggestion that the Tractatus is essentiallyan attempt to “liberate” us from a particular sort of confusion: theword erloesend, like its English counterpart, has an explicitly ethical orreligious connotation, carrying the sense of something that saves orredeems us; Wittgenstein himself uses a cognate of this word in con-nection with a discussion of the meaning of Christ’s Resurrection.38

One cannot but then wonder what place this sort of concern couldoccupy in the text as we have presented it thus far. There are, ofcourse, the relatively small number of remarks toward the end of theTractatus that explicitly address religious-sounding themes. But I be-lieve it is a mistake to seek to locate the ethical aspect of the worksolely or even primarily in these remarks; Wittgenstein, after all, im-plies that this aspect is something that is supposed to be made manifestby the text as a whole.39

It seems, then, that rather than viewing ethics as an additionalsubject matter treated by the Tractatus, for Wittgenstein we must cometo understand in a new light what we’ve already been doing in readingthis text. We must come to see the dialectical grappling with the limitsof sense as a fundamentally ethical struggle. The attempt to makeapparent this dimension of Wittgenstein’s thought will occupy us inthe last chapter of this book. Our aim here will not be to sum up andexplain the “real meaning” of the text (although the temptation to doso will be especially strong at this point), but only to bring out explic-itly what, for Wittgenstein, is properly an internal feature of philo-sophical inquiry.

V

One further set of questions needs to be addressed before we turn tothe details of the text. These concern the inevitable demand for amore complete justification of our approach to the Tractatus. Why mustwe take the difficulties in rendering the text coherent (discussed inSection II) to indicate the need for reading it in the dialectical mannerthat is here being urged? Is it not just this kind of incoherence thatmotivates the fundamental shift in Wittgenstein’s thought? Indeed,doesn’t our approach have the consequence of collapsing the distinc-tion between the early and later thinker – the distinction that Wittgen-stein himself time and again remarks on?

Introduction

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To the first question, the honest answer is a perhaps disappointingone: nothing ultimately compels one to read the Tractatus in the waythat I maintain. This, however, I do not take to be a shortcoming ofmy particular approach, but a feature of any interpretation of a philo-sophical work (a point, I believe, that Wittgenstein himself wouldinsist on). For at issue are fundamental intuitions about what kind ofthinker Wittgenstein at bottom really is – not straightforward “mis-takes” settled through the production of “proof text.” The legitimacyof our own particular approach can then only be established – or failto be established – in a wholesale manner, through its ability to dealwith the details of the text in a compelling manner, to render thewhole coherent. That, of course, is not to claim that such an abilityfunctions as a criterion of our interpretation’s adequacy. (The assertionthat a reading is acceptable because it renders the text more coherentis really no more than a grammatical remark in the sense of the laterWittgenstein.) Rather, I am simply saying that, in the end, our inter-pretation, like any textual interpretation, must wear its persuasivenesson its face.The other objections must be met more forcefully. For it is quite

reasonable to demand that a comprehensive interpretation be able toaccommodate Wittgenstein’s many post-Tractarian references to shiftsin his thinking; if our reading has the consequence that such remarksmust simply be dismissed, it cannot be entirely convincing. Let me beclear, then, that I by no means wish to downplay the significance ofWittgenstein’s claims to have changed his mind on various matters.On the contrary, one of the subaims of this study is just to shed somelight on this whole issue. What I shall seek to show, in general, is thatWittgenstein’s later self-criticisms are to be understood as the recogni-tion in his own thinking of the very philosophical demons the Tractatushad sought to completely exorcise. These criticisms do not take theform of a global reassessment of his overall philosophical aims but,rather, shifts in his understanding of rather specific points – the anal-ogy between a proposition and a picture, the role of the quantifier,the nature of analysis, and so forth.Of course, the very specificity of these criticisms has led many

commentators to understand them as revisions to a general philosoph-ical theory. Why would Wittgenstein be concerned with such details ifhe were truly committed to the ultimate nonsensicality of the ques-tions at issue?40 But I believe that we are here presented with a false

Introduction

19

dichotomy. And, indeed, from what we have said above it mightalready be apparent just why this is the case – that is, why matters ofdetail will loom large for Wittgenstein, even while his fundamentalphilosophical orientation remains the same. For if, as I maintain,“nonsense” is not a general or self-standing predicate for the Tractatus,if, that is, the assertion that such and such a claim does not makesense is related internally to the particular way its incoherence is mademanifest, then a precise characterization of the nature of that incoher-ence is all-important. To misdescribe the philosophical problem is in asense to miss the point – Wittgenstein’s own (real) point – entirely; itis to propagate the very confusions from which Wittgenstein aims toliberate us.41

For Wittgenstein, much will therefore be at stake in eliminatingwhat he comes to regard as the distortions in the Tractatus’ presenta-tion of the appropriate perspective – hence the dire character that heoften attributes to the “errors” in his early thought. In the course ofthis study, we shall then address some of these later corrections, andseek to understand them in light of our reading of the Tractatus. Andwhile these points about Wittgenstein’s development will in generalbe made in the footnotes, this should by no means be taken as indi-cating their lesser importance; the issue of the interplay between theearly and late philosopher instead informs our reading throughout.In what follows, we shall be immersed in very close textual analysis

of the Tractatus. The focus required to work through the internal intri-cacies of this difficult text will preclude our offering a great manyremarks as we go along about the broader project in which Wittgen-stein is engaged; that broader project, one hopes, will emerge throughthe details. And while I recognize that this sort of approach places ahigh demand on the reader, I believe it to be very much in the spiritof the philosopher at the center of our study.

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C H A P T E R I

PICTURES AND LOGICAL ATOMISM

I

The Tractatus opens with the famous declaration: “The world is every-thing that is the case” (TLP 1), followed by the qualification: “Theworld is the totality of facts (Tatsachen), not of things” (TLP 1.1). Oneis immediately struck by the dogmatic, absolutely authoritative toneof these claims. We do not at once know why they have been offeredup, or what the basis for asserting them might be, nor will any laterjustifications be provided. They present themselves, in the words ofthe Preface, as “unassailable and definitive” (TLP p. 28) – beyondreproach it seems, but also, perhaps, beyond proof. What is the stanceof the Tractatus? From what position are its absolute pronouncementsmade?One might suppose that such self-reflective questions would have

little relevance to the opening of the Tractatus. The text at this pointlooks entirely outward, on to the world; any concern with the condi-tions of its own utterance apparently falls outside of its purview. It isas if the author of the Tractatus were completely absorbed into theexternal reality that is here described – as if Wittgenstein were, so tospeak, presenting a realist’s perspective purely realistically. If that isthe case, however, we must recognize that this cannot itself be anunself-conscious move on his part. For at 5.634, after denying thatthere is an “a priori order of things,” he remarks: “Here it can be seenthat solipsism, when its implications are followed out strictly, coincideswith pure realism. The self of solipsism shrinks to a point withoutextension, and there remains the reality co-ordinated with it” (TLP5.64). “Realism” and “solipsism” (a term that, for Wittgenstein, is often


22

used synonymously with what we would ordinarily call “idealism”) donot refer to competing philosophical positions but, rather, to equiva-lent ways of describing the world. Unless we are to imagine him toshift radically his thinking in the course of the book, Wittgensteincannot then be understood as at the start straightforwardly advocatinga realist stance in opposition to some other philosophical position.1

Instead, it seems more accurate to see the opening as one means ofcharacterizing or exemplifying a perspective: the Tractatus is attempt-ing to adopt completely a certain way of looking at the world in orderto make manifest what that outlook comes to. And that suggests that,far from dismissing all questions about the nature of its own stance,this text from the very beginning brings such questions to the fore.The occurrence of the word “logic” at 2.012 and 2.0121 would then

appear to be significant. “In logic nothing is accidental: if a thing canoccur in an atomic fact the possibility of that atomic fact must alreadybe prejudged in the thing” (TLP 2.012). “Nothing in the province oflogic can be merely possible. Logic deals with every possibility, and allpossibilities are its facts” (TLP 2.0121). Wittgenstein is not here de-scribing a subject from afar but, rather, referring to the very activityin which he is engaged: the Tractatus is itself a logical inquiry, theperspective it adopts is the perspective of logic. This already beginsto throw light on the reasons for the text’s peculiar, seemingly dog-matic style. For a logical inquiry, as Wittgenstein conceives of it, wouldappear to be essentially different from a scientific investigation. Whilea scientific investigation seeks to determine what is the case, logicdeals only with the possibility of what is the case. The limits of logicare the limits of the possible. This suggests not only that it can makeno sense to speak of anything beyond logic but also that it makes nosense to speak of new domains within logic, of logical discoveries. Thefull expanse of logic must, in some sense, already be present to us. Abook on logic should not then contain arguments, as if it describednovel facts about whose existence we had to be convinced. Rather,one’s only concern can be to lay matters out perspicuously, to presentthings in such a way as to allow us to, as it were, recall whatwe already know. The apparent dogmatism of the Tractatus reflectsjust the utterly uncontroversial nature of the subject with which itdeals.The aim of the present chapter is then to bring out how the Tracta-

tus’ “ontological remarks” (TLP 1–2.063), as well as the first part of

Pictures and logical atomism

23

the picture theory, serve to clarify this “uncontroversial subject,” tobegin to make fully evident the real character of a logical inquiry. Nowsuch an interpretation might seem difficult to sustain, given that, afew scattered comments notwithstanding, “logic” as we ordinarily con-ceive of it – that is, as it is systematically presented in, say, Frege’sBegriffsschrift or Russell’s Principia Mathematica – is not treated by Witt-genstein until the 3s or even the 4s. Should we not then say that theearly discussion is merely preparatory, or that it serves, as Mouncesuggests, only to delineate how the world must be if there are propo-sitions and hence the possibility of logic?2 While these suggestionsmay sound tempting, I claim that they rest on too narrow a conceptionof what, for Wittgenstein (or, indeed, for Frege and Russell), logicconsists in. To be sure, the Tractatus does in one sense distinguishmathematical logic from the attempt to give a broader account of thatendeavor: this distinction is reflected in the text’s application of theterm “senseless” (sinnlos) to expressions of the form “p v �p,” but“nonsensical” (unsinnig) to expressions like “p is a proposition.”3 None-theless, as we shall see, mathematical logic is critiqued only insofar asit answers to the interests of logic in the broader sense – that is, insofaras it is put forward in the service of something like a Fregean projectof spelling out the “laws of thought.” It is always this inquiry into thefundamental possibilities of sense and nonsense that is of concern toWittgenstein in the Tractatus, and it is this that will represent ourconcern as well.

II

We can now begin to reflect in more detail on the fact/thing distinc-tion with which the text begins. Wittgenstein, in a later conversationwith Desmond Lee, offers this interpretation of the Tractatus’ openingremarks: “The world does not consist of a catalogue of things and factsabout them (like a catalogue of a show). . . . What the world is is givenby description and not by a list of objects” (CL 119). We might imaginea world consisting of objects a and b and a relation R. If our aim is todescribe accurately this world, it is not enough simply to offer a list ofthese constituents – this list would not distinguish a universe in whichaRb is the case from one in which bRa is the case. Instead, our descrip-tion must incorporate within it some acknowledgment of structure; itmust see the world as composed of facts, not things. Given the above


24

discussion, however, it would appear that the focus of logic cannot beon this structure, the obtaining of Tatsachen as such. For as 1.21 states(and 2.061 reiterates), facts are logically independent of one another:“Any [Tatsache] can either be the case or not be the case, and every-thing else remain the same” (TLP 1.21). Whether fact A obtains ordoes not obtain is then a contingent matter that is irrelevant to theperspective of the Tractatus. Logic’s concern, it would seem, must onlybe with the possibility of the Tatsachen, with what conditions theirobtaining or not obtaining.It is in connection with this idea that the notion of the object

(Gegenstand) must initially be understood. For, given what is held at 2and 2.01, one might otherwise wonder how the original primacy offact over thing is to be maintained. “What is the case, the fact (Tatsa-che) is the existence of atomic facts (Sachverhalten) (TLP 2). An atomicfact is a combination of objects (entities [Sachen], things [Dingen])”(TLP 2.01). The difficulty is that if these remarks are taken to meanthat a fact is made up of atomic facts and an atomic fact is made up ofobjects or things or entities (Wittgenstein makes it clear here that theseterms are interchangeable), then it appears that the world is, at bot-tom, composed of things not facts after all; we are back to conceivingof reality as describable by a list. It would seem, then, that while theprimacy of facts may not preclude all talk of objects, neither can thelatter be understood as a more basic constituent of the world. Instead,as becomes apparent when we reflect on the above conception oflogic, “fact” and “object” must be seen as standing at different levels:one’s hold on the notion of an object comes through a way of approach-ing what is the case, through looking at a series of facts with an eye towhat is common to them. To identify the objects is then not literallyto further decompose the world but, rather, to seek to grasp its logicalbasis, the condition of its possibility.4

Indeed, the notion of possibility is bound up with the Tractatus’initial account of the object:

Just as we cannot think of spatial objects at all apart from space, ortemporal objects apart from time, so we cannot think of any object apartfrom the possibility of its connexion with other things.If I can think of an object in the context of an atomic fact, I cannot thinkof it apart from the possibility of this context. (TLP 2.0121)If I know an object, then I also know all the possibilities of its occurrencein atomic facts.


25

(Every such possibility must lie in the nature of the object.)A new possibility cannot subsequently be found. (TLP 2.0123)

The point might be put as follows. It is constitutive of the object tooccur in an atomic fact, but not only in this fact; the object is under-stood just through its appearance in a whole series of facts and in thissense can be said to represent the “possibility” of any one of them.This is not, however, to suggest that the Tractarian object musttherefore be understood as dissolving simply into a possibility – as ifwe could understand the condition of the world apart from any con-sideration of how things actually stand. Instead, the object is this thingtaken against the background of all the rest of its possibilities of com-bination with other things. If “form” is understood, as 2.033 suggests,as the “possibility of structure,” then the object is not form alone, but,just as is stated of substance at 2.025, both form and content.5

It is useful to compare this conception of the object with Frege’s.Frege famously draws a distinction between the object and the func-tion – roughly, between that which corresponds to a proper name andthe “unsaturated,” predicative entity that combines with it. He em-phasizes the way in which the function does not stand on its own butis instead given by looking to what is common to a series of proposi-tions. Thus, he suggests that the real nature of the function could bemade apparent through the use of blank spaces for the argument placeof a functional expression, as when the expression “2x3 � x” is writtenas “2( )3 � ( ).” But while Frege goes on to contrast this idea of a“dependent” function with that of an object as a self-standing entity,one that is a “whole complete in itself,”6 the Tractatus’ aim would seemto be to bring out how no genuine logical distinction could be drawnbetween these notions; both function and (Fregean) object must beequally understood in terms of their capacity to occur in a space offacts. In this vein Wittgenstein remarks: “The thing is independent,insofar as it can occur in all possible states of affairs, but this form ofindependence is a form of connexion with the atomic fact, a form ofdependence” (TLP 2.0122). Thus, too, he asserts in the Notebooks:“Relations and properties, etc. are objects too” (NB 61).It seems that we should then say that Wittgensteinian objects com-

prise Frege’s objects, as well as his first-order functions, second-orderfunctions, and so forth. Of course, since these Fregean categories areset up in such a way as to be applicable to anything whatsoever that


26

can be said about the world, this cannot be altogether incorrect. Butinsofar as putting matters this way makes it appear that Wittgensteinis riding roughshod over Frege’s more fine-grained distinctions, thisformulation is misleading. For it is essential to recognize that theTractatus is not at the start attempting to tell us what sorts of thingsthere are; to introduce the notion of an object is not yet to haveidentified a logical kind. On the contrary, Wittgenstein’s emphasis oncombinatorial possibilities is meant to question the coherence of sucha priori categorization: what a given object is is only determined by thespecific range of its occurrences in atomic facts, that which 2.0141calls the “form of the object.” Thus he remarks:

Two objects of the same logical form are – apart from their externalproperties – only differentiated from one another in that they are differ-ent. (TLP 2.0233) Either a thing has properties which no other has, andthen one can distinguish it straight away from the others by a descrip-tion and refer to it; or, on the other hand, there are several things whichhave the totality of their properties in common, and then it is quiteimpossible to point to any one of them.For if a thing is not distinguished by anything, I cannot distinguish it –for otherwise it would be distinguished. (TLP 2.02331)

We have no way of establishing the identity of an object exceptthrough its particular capacities to combine with other objects. Toattempt to differentiate two objects with the same logical form is to dono more than to make a bare assertion of difference, a claim with nocontent.Still, one might wonder how the question of separating two objects

of the same logical form could initially arise, even in principle. Wouldthis not be like trying to ask whether this desk might be distinguishedfrom itself? We again recall, though, that objects are not merely form,but both form and content. It now begins to become apparent thatTractarian objects defy easy integration not only into a Fregean frame-work, but also into any sort of traditional philosophical framework.While we will no doubt be tempted to bring to bear notions like“particular,” “universal,” or “sense datum” to try to make sense ofwhat he has in mind,7 Wittgenstein will not allow us to rely on anysuch categories as basic, as clarificatory. Indeed, it would appear to bethe reverse: rather than seeking to understand objects in terms ofsome prior philosophical category, the Tractatus is suggesting that it is


27

only through their possibilities of occurrence that those fundamentalcategories emerge. The object is, we might say, a primitive notion.8

With this point in mind, we can then begin to understand the so-called argument for simples (2.02–2.0212), a series of remarks thathas received a good deal of treatment in the literature.9 It is useful toquote this difficult passage in its entirety:

The object is simple. (TLP 2.02)Every statement about complexes can be analyzed (zerlegen) into a state-ment about their constituent parts, and into those propositions whichcompletely describe the complexes. (TLP 2.0201)Objects form (bilden) the substance of the world. Therefore they cannotbe compound. (TLP 2.021)If the world had no substance, then whether a proposition had sensewould depend on whether another proposition was true. (TLP 2.0211)It would then be impossible to form a picture of the world (true orfalse). (TLP 2.0212)

If we take these remarks on their face, Wittgenstein could well seemto be adopting some variety of Russellian “logical atomism.” Like Rus-sell in The Philosophy of Logical Atomism, he assumes the possibility ofengaging in a process of logical analysis, a process that is imaginedeventually to terminate in entities entirely lacking in complexity. Suchsimple objects constitute the substance of the world, its necessarilyexistent logical core. But whereas Russell is then naturally led tospecify the nature of these endpoints of analysis – for him, logicalatoms comprise particulars, relations, and qualities – Wittgenstein, wehave just suggested, is essentially concerned to call into question thelegitimacy of this kind of a priori logical categorization. A very differentconception of simplicity would thus appear to be operating in theTractatus.If we are to bring out the real force of the Tractarian “argument for

simples,” we must then approach this passage with some care. Let usfirst focus on the idea of the “complex,” which appears in 2.0201. It isimportant to compare what that remark says about the notion with3.24, a claim that closely parallels 2.0201:

A proposition about a complex stands in internal relation to the propo-sition about its constituent part.A complex can only be given by its description, and this will either be


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right or wrong. The proposition in which there is mention of a complex,if this does not exist, becomes not nonsense but simply false. (TLP 3.24)

In holding that a statement about a nonexistent complex is false ratherthan nonsensical, Wittgenstein is saying that the existence of thatcomplex is irrelevant to the statement’s sense. And while weare by no means yet in a position where we can discuss in detailthe Tractatus’ conception of analysis,10 this claim, when taken togetherwith 2.0211, implies at the very least that analysis must involvesomething other than a process of decomposing complex objects intotheir basic constituents. After all, if some complex C were imagined tobe an entity literally made up of simple objects a and b, then C’snonexistence would entail the nonexistence of a and b. But since2.0211 holds that the existence of objects is a condition of the possi-bility of sense, then the proposition that makes mention of (nonex-isting) C becomes nonsensical. Again, though, that runs counter to3.24.By beginning to reflect on what it would mean to give an analysis,

then, we are led to draw a fundamental distinction between the com-plex and the object. To make that distinction evident can now be seento be the central purpose of 2.0201. Wittgenstein maintains there thata proposition about a complex can be analyzed into a statement aboutthat complex’s constituents, and this statement into a number of prop-ositions that then completely describe that complex. Now a morecomplete account of exactly what procedure he has in mind at thispoint must await our discussion in the next chapter. Already, though,this remark can be seen to bring out how the complexity of thecomplex, so to speak, is ultimately (i.e., on completion of an analysis)absorbed into a series of propositions. The complex, in other words, isnot to be treated, from a logical perspective, as one kind of entityamong others in the world, one whose composition is essential to itsnature. Instead, the very possibility of describing such an entity showsthat it is really not an entity at all, but a structure – the obtaining orholding of entities.11 For Wittgenstein, the apparent “reference” to acomplex in the unanalyzed proposition marks a disguised allusion toa fact or set of facts.12

But if complexity is in this way always associated with the holdingof facts, it then would appear that the object cannot but be simple –that there are no logical objects or entities other than simple ones.13


29

And, indeed, on reflection, we see that this point follows from theconception of the Tractarian object as constituted by its possibilities ofcombining with other things. For this is just to maintain that an objectshorn of some of its combinatorial possibilities – that is, an object thatis further decomposed – will no longer be the same entity.Wittgenstein, in holding at 2.021 that objects as the substance of theworld “cannot be compound,” must ultimately be understood as sug-gesting that predicating complexity of a logical entity can make nosense.The contrast of the Tractatus’ logical atomism with the Russellian

version thus becomes striking. For Russell, the goal of logical analysisis to specify the sorts of objects that satisfy certain conditions: weidentify the genuine simples when we distinguish from complex enti-ties those objects that are incapable of definition and are insteadknown only by direct “acquaintance.” In the Tractatus, though, ourproper aim is not to seek the right kinds of entities, but rather to revealclearly the logical role or function of that which is before us; logic, wemight say, views the world always through the lens of simplicity.Wittgensteinian analysis must then be seen purely as an attempt todescribe the world in such a way as to render perspicuous its simple,logical core. Thus, Wittgenstein remarks in the Notebooks:

If, e.g., I call some rod “A” and a ball “B,” I can say that A is leaningagainst the wall, but not B. Here the internal nature of A and B comesinto view.A name designating an object thereby stands in a relation to it which iswholly determined by the logical kind of the object and which charac-terizes that logical kind.

Again, it is assumed that the identity of the object, as far as logic isconcerned, is determined by the possibilities of its occurrence in aseries of atomic facts. If we are to adopt the point of view of logic, itmust then be evident from the role of the name in any given contextalone just what the object it designates is – no additional contexts ofits occurrence need be considered. So, for example, if “A” in thepassage above were a genuine name, then A would appear in theatomic fact as leaning or even, perhaps, as leaning against a wall. Itcould not also occur as, say, a colored object, or something with aweight; that is, it could not have any such form and remain A. Solelyfrom the functioning of the name “A” in the elementary proposition


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representing that atomic fact, the essential nature of this object be-comes manifest.We now can begin to see why Wittgenstein insists on the existence

of that “substance” that the simple objects are said to form or consti-tute. For what would it mean to suppose that there might not beobjects in this sense? It is useful to compare such a scenario with thepossible nonexistence of a complex. As we saw above, 3.24 maintainsthat a proposition that makes mention of a nonexisting complex isfalse rather than nonsensical. If we understand talk of a “complex” asreflecting the confusion of a gesture toward a structure with a refer-ence to a logically compound entity, the reason for this claim becomesapparent: the nonexistence of a complex is equivalent to the nonob-taining of a fact or series of facts. But the situation is otherwise withregard to an object. In denying that a genuine name has reference, weare not raising the possibility that one occurrence of an object doesnot exist – that is simply to imagine the nonobtaining of some atomicfact. Instead, given the Tractatus’ conception of the object, what herewould be suggested is that a whole space of possible occurrences mightnot be given. In Fregean terms, it would be as if one were to supposenot that a function did not hold for some argument, but that theargument place itself, the possibility of an argument, were not avail-able. To deny the existence of substance is to call into question thevery possibility of the representation of atomic facts.Wittgenstein suggests that it is nonsensical to imagine such a possi-

bility. The denial of substance, he claims, is tantamount to making thesense of a proposition dependent on the truth of another proposition.This is just to say that if the possibilities of representation were notalready secured in advance, it would always be an open question as towhether a given fact could be represented. Without the givenness ofobjects, we would not be able to say that, for example, A is leaningagainst the wall until we first knew that A was the kind of thing thatwas capable of occurring in this context. But since the propositionexpressing that knowledge would be subject to the same indefinitenessof sense, an infinite regress would then ensue. And in this case, as2.0121 maintains, it would be impossible to form a picture of theworld, true or false.Notice, then, that the point here does not, as some commentators

have suggested, turn on a worry over the holding of the connection


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between the name and the object – as if Wittgenstein were claimingthat, without a guarantee of immediate contact between language andthe world, it would never be certain as to whether our names reallydid refer.14 No such problem of reference is at issue in the Tractatus.For Wittgenstein, instead, the real concern is with the fundamentalascriptions that can be made to the world, the possibilities that allowthe facts to stand in the way they do. The requirement for substanceis ultimately nothing but the insistence that nothing underlies or con-ditions logic, that logic is, as it were, self-subsistent.15 It is just this ideathat is expressed in the characterization of substance as “what existsindependently of what is the case” (TLP 2.024).Now, it is not yet clear how this claim about the need for the logical

possibilities of the world to be given in advance coheres with what wehave said to be Wittgenstein’s questioning of any attempt at a priorilogical categorization; this tension only begins to resolve itself in theaccount of the picture. But the above discussion does allow us to gaina better grasp on the notion of the atomic fact:

The object is the fixed, the existent; the configuration is the changing,the variable. (TLP 2.0271)The configuration of the objects forms the atomic fact. (TLP 2.0272)In the atomic fact objects hang in another, like the links of a chain. (TLP2.03)

The atomic fact is in its essence an arrangement of objects. To say thatthese objects hang in one another like the links of a chain is toemphasize that no further elements are involved in this configuration,no additional “relations” to bind together its components: the atomicfact is constituted solely by the objects being arranged in thisway. Thatparticular arrangement 2.032 terms the “structure” of the Sachverhalt;the structure thus consists in how the objects hang together. Of course,since the identity of the object is determined by all its possibilities ofcombining, any single occurrence of an object – any particular way ofits hanging in an atomic fact – does not exhaust its nature. But fromthe above preliminary points about analysis, it would seem that thisnature (the form of the object) should nonetheless at least be evidentthrough any one of those occurrences. In other words, the particularway that the object does lie in the atomic fact must reveal clearly justhow it can lie – which is to say, what, from a logical perspective, it


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essentially is. 2.033 describes “form” as “the possibility of structure.”The atomic fact, one could say, presents its structure precisely in sucha way as to make the forms of its constituents manifest.It thus becomes apparent that the requirement for objects and the

postulation of atomic facts are closely linked; both, it would seem, aredemands of the logical inquiry itself. To postulate the possibility ofdescribing what is the case (the totality of Tatsachen) in terms of theexistence of atomic facts is simply to suppose the possibility of a per-spicuous presentation of the logical dimension of the world, its neces-sarily existent core. At the same time, however, reflection on this ideabegins to reveal the peculiar nature of the inquiry into that “existentcore.” For it would appear that, even in the atomic fact, substance ispresented only indirectly, emerging through the structure, through theway in which things stand. Rather than constituting an ordinary sub-ject with its own special area of concern, then, the inquiry into sub-stance seems ultimately to represent no more than a perspective onthe world, a way of viewing what is the case. And that would suggestthat, already, the Tractatus is leading us to call into question the fun-damental supposition of the thought of Frege and Russell – the sup-position that logic constitutes a genuine science.Still, it must be acknowledged that the real nature of the question

that the Tractatus is pursuing remains at this point abstract, indis-tinct. It is, I claim, the central aim of the subsequent discussion ofthe picture to bring that question – the fundamental question oflogic – into sharper focus.16 Of course, such an interpretation runscounter to the standard way of approaching the “picture theory”(so-called). On the standard view, the introduction of the picturerepresents the Tractatus’ shift from ontology to the concern with lan-guage, the concern that occupies the text from that point on.17 Butwhile it is undeniable that the notion of the picture is meant toshed light on the proposition – propositions are explicitly describedas pictures at 4.01 – it is not so clear that such a focus represents agenuine departure from the focus at the opening of the text. Cer-tainly the Notebooks does not recognize a sharp distinction betweenan investigation into the proposition and an investigation into theworld: “My whole task consists in explaining the nature of the prop-osition. That is to say, in giving the nature of all facts, whose picturethe proposition is. In giving the nature of all being” (NB 39). Simi-larly, several remarks in the Tractatus appear to emphasize how the


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text’s early claims about the world can be interchanged with pointsabout language:

The thing is independent, in so far as it can occur in all possible circum-stances, but this form of independence is a form of connexion with theatomic fact, a form of dependence. (It is impossible for words to occurin two different ways, alone and in the proposition.) (TLP 2.0122)A spatial object must lie in infinite space. (A point in space is an argu-ment place.) (TLP 2.0131)

Indeed, when we reflect on our own interpretation of the openingpassages, we note how it also has been bound up with linguisticnotions – how the notions of fact, object, and atomic fact have beenexplicated only through talk of propositions and names. This inter-twining of the putatively independent notions of language and worldwould thus seem to be intrinsic to the Tractatus’ understanding of thelogical perspective. And this suggests that rather than marking a sud-den shift in the direction of the text, the account of the picture isreally only a deepening, a clarification of the same inquiry that isinitiated at the start.

III

In keeping with this overall approach, we can then understand theintroduction of the notion of the picture as immediately motivated bycertain tensions in the remarks that close the 2.0s. First, we note theseemingly shifting sense of the term “world.” In 2.04, “the world” isidentified with the totality of existent atomic facts (die Gesamtheit derbestehen den Sachverhalte). Given the text’s initial association of theworld with all that is the case (TLP 1), all that is the case with thetotality of facts (TLP 1.1), and this totality with the existence of atomicfacts (TLP 2), we might have assumed that the totality of existentatomic facts constitutes the limit of the world. The subsequent intro-duction of the term “reality,” a notion with an apparent wider exten-sion than “the world,” then comes as a surprise: “The existence andnonexistence of atomic facts is the reality” (TLP 2.06; italics mine). IsWittgenstein imagining atomic facts that lie outside of the world? Theidea is in itself strange enough. But it would also seem to blur theTractatus’ fundamental distinction between the fact as what happensto obtain and the object as its logical condition. For it is very tempting


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to view the nonexistent atomic fact – the fact that is not but could be –as in some sense another condition of the possibility of the (existent)atomic fact. Or, equally complicating matters, we may maintain thedistinction between a fact and its condition, but then feel driven toposit possible objects (possible possibilities as it were) as the logicalbases of these nonexistent, merely possible facts.Wittgenstein’s position becomes still more puzzling when we look

at the supposed further clarification of 2.06 provided by 2.063: “Thetotal reality is the world” (TLP 2.063). The just introduced distinctionbetween “reality” and “the world” is now apparently denied or insome sense overcome; the Tractatus would seem both to propose theexistence of facts outside of the world and to imply that such an ideadoesn’t make any sense. Why this equivocation? What is the status ofthe “negative fact,” as Wittgenstein refers to the nonexistent atomicfact at 2.06? It is, it would seem, some version of the ancient problemof the nature of “what is not” that confronts us at the close of the2.06s.A second tension in the remarks ending the 2.0s centers around the

question of the relation between atomic facts. At 2.062, in keepingwith the 1.21s claim of the logical independence of facts, Wittgensteinclaims: “From the existence or nonexistence of an atomic fact wecannot infer the existence or nonexistence of another” (TLP 2.062).This assertion, however, would seem to run counter what is main-tained just three remarks previously: “The totality of existent atomicfacts also determines which atomic facts do not exist” (TLP 2.05). Onewonders how one set of facts can “determine” a second set if thesefacts are entirely independent of each other. It might be tempting tosuppose that Wittgenstein is introducing the possibility of a relation ofdetermination distinct from one of logical inference. But that would flyin the face of 6.37: “A necessity for one thing to happen becauseanother has happened does not exist. There is only logical necessity”(TLP 6.37). The solution, it then seems, is that we cannot view positiveand negative atomic facts as separate or independent notions: we caninfer the nonexistence of A from the existence of A (A “determines”�A) just because, from the perspective of A, �A does not count asanother fact.Once more, then, we run up against the intrinsically ambiguous

status of what is not. It now appears that this difficulty is connectedwith the notion of logical inference: the possibility of logical relations


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between facts, of a “reality” that extends beyond the limits of theworld, and of nonexistent Sachverhalten are all closely linked. It isthrough the picture theory that we begin to see how this cluster ofnotions relates to the attempt to understand the unchanging substanceat the heart of the world.

The move to a discussion of pictures is initiated abruptly, without anyexplanation: “We make to ourselves pictures of facts” (TLP 2.1). It isimportant to note at once the emphasis here on picturing as an activ-ity: we make pictures of facts and to ourselves, for our own purposes.From the beginning, it would seem, Wittgenstein is viewing the pic-ture not as an autonomous, self-interpreting entity, but rather assomething to be viewed within the context of its use.18 This emphasisis made even more explicit by Wittgenstein in a later conversationabout the Tractatus with Waismann. After suggesting that the Tractatus’notion of a picture was used to highlight certain important features ofa proposition, Wittgenstein goes on: “I could also use a measuring-rodas a symbol, that is, insert a measuring-rod into a description and useit in the same way as a proposition. You may even say, In manyrespects a proposition behaves just like a measuring-rod, and thereforeI might just as well have called propositions measuring-rods” (VC185). To speak of a measuring-rod is of course to speak of somethingthat cannot be understood apart from its connection with humanpurposefulness – presumably no one will suppose that a ruler mightapply itself to the object to be measured. We note, then, that theTractatus does in fact at 2.1512 draw the analogy between a picture anda measuring rod (Masstab). The above passage would appear to suggest– and our later discussion will make clear – that the comparison is tobe taken quite seriously, that it gives us the aspect of the picture thatis crucial for Wittgenstein’s whole account.The significance of this emphasis on the picture as it is used is not

yet apparent. But we shall see how some such idea will be essential inmaking sense of the next several remarks. First, then, 2.11: “Thepicture presents (vorstellt)19 the states of affairs (Sachlage) in logicalspace, the existence and nonexistence of atomic facts (Sachverhalten)”(TLP 2.11). The reference here to “logical space” recalls 1.13: “Thefacts (Tatsachen) in logical space are the world.” From the start, itwould seem, the world is understood always against a larger – logical –backdrop of what is not the case.20 Still, taken as it stands, 2.11 makes


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the problem of nonexistent facts seem yet more mysterious. Howcould the picture considered in itself present a negative fact? Is what isnot present in the picture imagined also to be part of what it presents?The elements of the picture stand for (vertreten; “go proxy for”) things(TLP 2.131), but this seems to say nothing about the possibility ofrepresenting facts that do not exist, or at least that do not exist in theconfiguration presented by the picture.It is 2.15 that allows us to begin to understand the fundamental

direction of Wittgenstein’s account: “That the elements of the pictureare combined (verhalten) with one another in a definite way presents(vorstellt) that the things are so combined with one another.” Thepicture, as 2.141 states, is a fact and it would seem to be just this“facticity” that allows it to portray. Now clearly Wittgenstein is hereimplicitly challenging Frege’s assimilation of a proposition to a name,as is often noted:21 propositions as pictorial facts must be sharply distin-guished from names, which, as analogues to the pictorial elements,serve only as proxies for objects. But it is essential to understand thereal purpose of Wittgenstein’s attack on the Fregean conception. Forthe temptation amongst commentators is to suggest, even while point-ing out Wittgenstein’s difference with Frege, that the Tractatus is hereultimately concerned with the problem of how some particular picturefact can be connected with the appropriate world fact. Thus, Black, forexample, sees the picture theory as an attempt to give an account ofhow the relational proposition “aRb” could mean that some specificstate of affairs cSd obtains.22 To state the problem in this way, how-ever, is just to reiterate the Fregean construal of the proposition (pic-ture) as a kind of name (i.e., pictorial element). It is to view the senseof the picture as something to which the picture corresponds, a kind ofentity to which that picture must somehow be securely fastened. And,indeed, we can now see how such a Fregean view is connected withthe perplexity over the issue of negative facts. For on this conceptionwe are naturally led to wonder what it is that can constitute thereference of pictures that depict facts that do not obtain. It is then ashort step – a step not actually taken by Frege himself, but one toyedwith by Russell23 – to begin postulating a special domain of nonexis-tent facts, a shadowy realm of all that is not but could be.Wittgenstein’s emphasis on the facticity of the picture is in part

meant to get at the confusion that would bring us to make such a


37

move. Rather than leading us to imagine picturing as a relation be-tween a new kind of entity – facts – we are urged to see that no realrelation is at issue in the first place. Wittgenstein states that it is justthat these proxies for objects stand to each other in the way they dothat says things in the world so stand. This is meant to bring out thatwhat is doing the expressing cannot be the set of pictorial proxies assuch, but rather our having taken these proxies as a certain kind offact about the world. To speak meaningfully of the picture as a “modelof reality” (TLP 2.12) thus presupposes understanding the picturewithin the context of its application; the picture, we might say, is in acertain sense an abstraction from the process of picturing. But then ifour concern is to explain how the picture is, as it were, articulate, howit can express something about the world, it becomes apparent thattalk of reference is completely beside the point. For what we seek isnot dependent on the existence or nonexistence of some entity, but isinstead part of what it means to have a picture in the first place.With this emphasis on the activity of picturing in place we can now

better understand remark 2.11: “The picture presents (vorstellt) thestates of affairs (Sachlage) in logical space, the existence and nonexist-ence of atomic facts (Sachverhalten).” In speaking there of what thepicture “presents,” Wittgenstein is conceiving of the picture in relationto all those atomic facts it can be used to represent. The picture presentsthe existence and nonexistence of atomic facts precisely because it isthe same picture that allows us to say that some fact either is or is notthe case. This idea Wittgenstein indeed comes back to over and overagain in the Notebooks. Compare, for example, these remarks fromNovember 1914:

That two people are not fighting can be represented by representingthem as not fighting and also by representing them as fighting andsaying that the picture shows how things are not. We could represent bymeans of negative facts just as much as by means of positive ones. (NB23)In order for it to be possible for a negative atomic fact (Sachverhalt) tobe given, the picture of the positive atomic fact must be given. (NB 24)Negation refers to the finished sense of the negated proposition and notto its way of representing. If a picture represents what-is-not-the-casein the aforementioned way, this only happens through its representingthat which is not the case. For the picture says, as it were: ‘This is how it


38

is not’, and to the question “How is it not?” just the positive propositionis the answer. (NB 25)

The point would seem to be to emphasize the way in which thenegative fact is dependent on, or given entirely by means of, its posi-tive counterpart. In conceiving of matters in this manner we will befar less tempted to reify the negative fact, to attribute to it some specialontological status. (And here we should recall Wittgenstein’s initiallysuggesting that the negative fact lies in some sense outside the world.)At the same time, we see that from the point of view of logic there isnothing sacrosanct about the existent fact either; positive and negativefact stand on the same level, a contrast between two uses of a picture.(This was the point of Wittgenstein’s identifying the total reality andthe world at 2.063.) Positive and negative fact are coequal inhabitantsof logical space, introduced together at 2.11.The effect of this whole discussion is then to bring into sharper

focus the question which Wittgenstein believes is really at stake in thiscontext. In recognizing the interdependence of positive and negativefact, we see that our concern here must be to go, as it were, behindthese facts, to account for the possibility of both together. That is,rather than attempting to explain how a particular picture can cor-rectly designate some fact in the world, the Tractatus suggests that logicmust properly inquire into the possibility of representation, true orfalse. The question that the picture theory begins to bring into relief isthen the question Wittgenstein poses early on in the Notebooks: “Whatis the ground of our – certainly well founded – confidence that weshall be able to express any sense we like in our two-dimensionalscript?” (NB 6). What we want to explain ultimately, in other words,is how our propositions are capable of representing all and only statesof affairs in the world, how it is that our propositions are guaranteedto make sense in the first place. But that is to say that what is reallyat issue here is just the question of the nature of the fundamentalcategories in terms of which the world is constituted – for the Tractatus,the question of the nature of substance itself. It is in the next severalremarks that we see the core of Wittgenstein’s response.In the present context, then, the problem will have to do with

giving some sort of specification of the possibility of the picture’s“presenting” (in Wittgenstein’s special sense of this term)24 what itdoes. Now the possibility of the pictorial fact, of the particular deter-


39

minate structure itself, the Tractatus calls the picture’s “pictorial form”(Form der Abbildung; TLP 2.15). 2.151 states that this pictorial form isalso the possibility of the things being related to each other in thesame way. The pictorial fact and the world fact that it representswould thus seem to operate within the same space of possibility. And,indeed, just that this is the case is standardly taken to be the centralcontention of the picture theory.25 Wittgenstein’s answer to the ques-tion of how the picture – and hence language – can always be aboutthe world is thus supposedly to be: they share a form.Still, while I certainly do not deny that Wittgenstein speaks of

something in common between the picture and what is pictured – thisis explicitly asserted at 2.16 and 2.161 – the important question con-cerns his attitude toward this claim. In that regard, I insist that, as anexplanation of how the picture is always capable of depicting the world,the strategy of taking recourse in talk of an isomorphism is empty; itamounts to no more than the claim that depicting the world is possiblebecause the world has the possibility of being depicted. One mightusefully compare Wittgenstein’s approach here with the Russellianpostulation of particulars, qualities, and relations as the ultimate “sim-ples,” or even with the Kantian attempt to specify the fundamentalcategories that constitute the phenomenal world. The Tractatus’ asser-tion of the isomorphism between the picture and reality cannot beunderstood as an effort to offer the basis of an alternative answer tothe ones provided by Russell and Kant but, rather, just as a way ofexpressing the absence of any such answer. This then implies that ourproper aim here must be to understand how we are driven into mak-ing this empty assertion, why it is for Wittgenstein that we cannot atthis level draw a meaningful distinction between the picture and whatit depicts.26

Toward that end, let us first seek to become clearer on what itwould mean to specify the picture’s pictorial form. What is wanted, itwould seem, is an account of the coordination of pictorial elementsand objects referred to at 2.13 and 2.131, the coordination that 2.1514terms the picture’s “pictorial relationship” (die abbildende Beziehung).Now clearly one dimension of this correlation, the choice of particularpictorial representatives, is arbitrary: if my aim is to represent a booklying on a table, it is entirely up to me whether to use rectangles,squares, color patches or what have you to stand for the objects com-posing that fact. Wittgenstein, at 2.131, uses the term vertreten (“The


40

elements of the picture stand [vertreten], in the picture, for the ob-jects”) to designate this connection between pictorial element (and,later, name) and thing; it is by means of the vertreten relation thatwhat is earlier called the “content” of the object comes into view. Butsetting up this sort of arbitrary correlation would not by itself seemsufficient to ensure that any picture I construct will portray a possiblestate of affairs. What is to stop me from, for example, placing a picto-rial representative of an event into a pictorial representative of a hole,27

or picturing a situation in which red is louder than green? Evidently,the assuming of a particular outward appearance is not enough toguarantee that a set of correlated pictorial elements is a genuine pic-ture in the Tractatus’ sense of the term.28 Only if the pictorial represen-tatives have all the same possibilities of combination as their real worldcounterparts – only if they have the same form as those objects – willwe say that they are really representatives of the latter. The legitimacyof the arbitrary correlations we set up would appear to depend insome sense on a deeper coordination of form.29

The Form der Abbildung has to do just with this idea of a non-arbitrary, inner connection of the picture and reality. As the possibili-ties of combination common to the pictorial elements and the objectsthey stand for, it constitutes the ultimate ground of our ability topicture the world. In laying bare the pictorial form, the forms of theobjects, it then seems that we would come to see the essence of repre-sentation; that is, the a priori core both of our means of representingand of what is represented. And that is to say that the specification ofthe pictorial form would constitute a large step toward the fulfillmentof one of the most fundamental tasks of philosophy, as traditionallyconceived.Wittgenstein’s way of attempting to drain this whole inquiry of its

philosophical allure – the basis of his “solution” to the problem of thenature of substance – begins to become apparent when we closelyconsider remarks 2.151 through 2.1512:

The pictorial form is the possibility that the things are so combined withone another as are the elements of the picture. (TLP 2.151)That is how a picture is attached to reality; it reaches right out to it. (TLP2.1511)It is laid against reality like a measure (ein Masstab – i.e., a ruler). (TLP21512)


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We must once more ask ourselves what it means to compare a picturewith a ruler. A useful way of approaching this question is suggestedby remarks 43 and 44 of the Philosophical Remarks. Here, after againstressing the importance of the picture-ruler comparison, Wittgensteinpoints out that the possibility of measuring in general does not presup-pose a particular length for the object to be measured. All that isnecessary is for me to have a way of using the ruler, of applying it tothe world.30 The Tractatus similarly suggests that the possibility of de-picting in general does not assume the existence of some fact or otherin the world, but only a way of picturing – a way of projecting ourpictures. And since, as we have seen, our hold on the picture isparasitic on a notion of the picture in use, that method of projectioncan be said to be in a certain sense already given, once we are giventhe pictorial fact. It would then follow that a picture, simply in virtueof being a picture in the Tractatus’ sense, must always present somepossible state of affairs. This indeed is just what Wittgenstein suggestsat 2.1513: “According to this view the pictorial relationship whichmakes it a picture also belongs to the picture.” The point, in otherwords, is that what makes something into a picture of the world – thepictorial elements being correlated with the things they stand for – isalso what makes it into a picture in the first place. Conceived in thisway, a picture is seen to carry within it its inner coordinations withreality and thus cannot fail to depict.31

To say that the inner coordinations with reality are part of thepicture, however, is at the same time to suggest the insubstantiality ofthe pictorial form. (As always in the Tractatus, the appearance of sub-stantial necessity – in this case the necessity of the picture’s attachmentto the world – is a mark of one’s failure to have made a genuineclaim.) For what Wittgenstein’s account is meant to bring out is thatthe essential possibilities of combination common to the pictorial ele-ments and the objects are given, as it were, after the fact, preciselythrough the projection of the picture on to reality.32 Rather than havingan a priori, normative status, the pictorial form is parasitic on our wayof picturing with a picture.Wittgenstein’s point can be brought into sharper focus if we reflect

on the notion of space, one of the pictorial forms referred to at 2.171.33

The above discussion is meant to get us to see the incoherence ofsupposing that in order to construct a spatial picture we must “have”beforehand a notion of space to function as a kind of constraint. It is


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not, in other words, as if in constructing a picture of, say, a book lyingon a table, I must take care to have chosen proxies not only for theseobjects, but also for their capacity to assume spatial relations. Instead,that these objects are in space – their spatial form – is revealed throughmy being able to construct a picture in the first place: the fact thatthese two shapes can be correlated with that book and that table insuch a way as to make a genuine picture gives us part of what wemean by “space.” The limits of my ability to make a picture of thiskind then constitute the limits of my notion of spatiality – which is tosay that this pictorial form is not a constituent of a given picture, butpart of its way of being related to the world, part of what this pictureis. And that would seem to be just another way of stating the point of2.172: “A picture, however, cannot depict its pictorial form: it showsit forth” (weist sie auf).

IV

The central Tractarian notion of showing is thus introduced at thecrucial moment in the discussion of the picture. Viewed in isolation,this idea naturally leads us to imagine the existence of necessary, butineffable features of reality. With the above considerations in mind,however, we see that the real aim of the Tractatus is to turn such anidea on its head; we see that the show/say distinction functions as partof the attempt to dissipate the urge to look for any such “necessaryfeatures.” For it now becomes apparent that the assertion that thepictorial form can only be shown is equivalent to claiming that every-thing logic would want to say about the a priori nature of pictorialrepresentation is a feature of how we operate with the picture. Ratherthan tantalizing us with the notion of an intrinsically inexpressibledimension to reality, the real point here is then to bring out theemptiness of the question motivating our whole inquiry. But noticethat, without the demand put forward in that question, the idea thatthere is any contrast with “what can be said” has no role whatsoever.That is, to put it somewhat crudely, it is simply pointless to state as ageneral, self-standing claim either that something is or that somethingis not shown by this picture of a book lying on a table. Instead, thepossibility of introducing this language is dependent on the logician’sdesire to get at the essence of representation, his sense that there is,


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in this respect, a gap in our understanding of the world; the show/saydistinction, we might say, serves as a response to him.We now begin to see more concretely what we described in the

Introduction as the fundamentally “dialectical” nature of the Tractatus’argument – the way in which its central notions only have their lifein relation to the philosophical temptations that the book aims toeradicate.34 The point in the present context can be made still clearerif we consider for a moment a more standard interpretation of the roleof the show/say distinction in the picture theory.35 Such an approachtends to treat that which is shown by the picture as a kind of unstate-able presupposition of what the picture represents. Pears provides agood illustration of this view:

[Wittgenstein believed that] the possibility of saying some things infactual discourse depends on the actuality of other things which cannotbe said. Then the analogy with pictures was used to illustrate the depen-dence of the sayable on the unsayable: a portrait relies on the projectivegeometry which links the canvas to the sitter, but it does not include adiagram of that linkage.36

One’s immediate response here might be to wonder why a secondpicture could not be used to represent the linkage between the canvasand the sitter.37 Pears’s answer is that, while this is of course possible,any such picture would ultimately have to “pick out the same factsabout the sitter and use the same method of projection in order topick them out.”38 The link between the picture and the world thusmust seemingly defy all attempts at being fully represented, at least inany sort of informative way. This implies, for Pears’s Wittgenstein, amore general restriction on our language’s capacity to represent: thepicture theory is ultimately construed as suggesting the impossibilityof giving “a complete account of the sense of any factual sentence.”39

Now the question of just how the picture theory is to be extendedto language in general we have yet to discuss. But already we can seethe way in which Pears’s reading assumes a quite substantial or robustconception of the “unsayable.” The pictorial form, while somehow notcapturable in any picture, nonetheless has “actuality” as a kind of deepfact on which the possibility of depicting more superficial facts ulti-mately “depends.” To be sure, Pears will construe the necessary inex-pressibility of the pictorial form as part of the Tractatus’ attempt to


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place a limit on meaningful discourse. In this sense, he might wellagree with my claim that the show/say distinction forms the heart ofWittgenstein’s attack on the possibility of an inquiry into the essenceof the world and its representation. But we must see that it would, inthis case, constitute a very different sort of attack. After all, nothingabout the Pears’s construal of the picture theory suggests that therewould be anything nonsensical about the attempt to give an articulationof pictorial form. At best, Wittgenstein could only show that we areincapable of adopting the sort of external vantage point from which a“complete” – and this presumably must mean nonredundant – depic-tion of the underlying, evidently quite real, ground of representationcould be given. On the Pears reading, then, the picture theory wouldserve to present the logico-philosophical investigation into the groundof representation as fundamentally coherent, but as in the end unsat-isfiable.My claim, however, is that Wittgenstein’s real focus is not on the

satisfiability of logic’s project, but on the possibility of coherently imag-ining such a project in the first place. The Tractatus holds that thepicture “must have in common” with reality its pictorial form “in orderto depict (abbilden) it – correctly or incorrectly – in the way that itdoes” (TLP 2.17). The temptation to which Pears succumbs is to sup-pose that the depicting relation – the relation between the picture andwhat it is in general directed toward40 – is here being treated as some-how undergirded by the pictorial form: the pictorial form constitutes amysterious third element, a kind of metaphysical glue linking thepicture and reality. But we have seen that the actual purpose of thepicture theory is just to lead us away from such a view. Far from beingimagined as a third element, stateable or unstateable, the pictorialform is no element at all, but rather part of the picture’s way ofdepicting. The picture “must” have in common with reality its partic-ular pictorial form precisely because this form is constituted by thispicture’s application to the world – just as the possibilities of lengthare given through the ruler’s use in measuring magnitudes. This, ofcourse, is not to construe that form as a kind of full-bodied entityresting tantalizingly just beyond human reach, nor, indeed, to putforward any sort of “claim” that could coherently be challenged. In-stead, the point only has force when we recognize in it the fundamen-tal question of logic. Its purpose is served if we see that the inquiry inwhich we have thought ourselves to be engaged is predicated on


45

imagining a kind of division between the essential possibilities of theworld and the means by which these are represented. To acknowledgethat the pictorial form can only be shown is to acknowledge theincoherence of the attempt to draw such a division.

Still, with the assertion of the inexpressibility of the pictorial formwe have by no means exhausted the Tractatus’ discussion of the pic-ture. Wittgenstein goes on to introduce the notions of sense, truth andfalsity, logical picture, and the “representing” – as opposed to the“presenting” – dimension of the picture; the significance of these no-tions must be explored. Moreover, we have yet to see exactly how theabove account is meant to apply to the proposition, how the initialpoints about the picture, as well those about the world and the natureof objects, will appear within the context of a more explicitly “linguis-tic” discussion. It is to the latter issue that we shall turn in the nextchapter.

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C H A P T E R I I

WHAT IS ANALYSIS?

I

Wittgenstein’s declaration of the inexpressibility of the pictorial format 2.172 and 2.174 is followed by the introduction of a new notion –the logical form: “What every picture, of whatever form, must have incommon with reality in order to be able to depict (abbilden) it at all –rightly or falsely – is the logical form (die logische Form), that is, theform of reality” (TLP 2.18). With this mention of “reality,” we are ofcourse called back to the discussion at the beginning of the picturetheory. The notion of reality, we have seen, is connected with theexistence and nonexistence of atomic facts, which is to say with every-thing that the picture can be used to depict. It is not at once clear,however, just how such an idea would differentiate the logical formfrom the pictorial, if Wittgenstein does in fact intend to distinguish thetwo. After all, the claim that the picture must share with the reality itdepicts a pictorial form is central to the picture theory. What is thepurpose of holding that there is also common to the picture and realityanother kind of form?The basis of Wittgenstein’s answer is suggested by the next two

remarks: “If the pictorial form is the logical form, then the picture iscalled a logical picture” (TLP 2.181). “Every picture is also a logicalpicture. (On the other hand, for example, not every picture is spatial.)”(TLP 2.182). On this account, the logical form appears in some senseto contain the pictorial form: every spatial picture is to be construedas a logical picture, but not every logical picture is spatial (or temporalor colored). “Logical form” is thus to be understood as a more generalterm for the representational possibilities of any picture. But if this is

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the case, the notion of pictorial form appears to become unnecessary;it seems we should call all pictures “logical” and speak only of logicalform.1 Or are we to assume, as Friedlander seems to, that “logicalform” describes something not only more general, but also additionalto the pictorial form – a feature of the picture on top of its Form derAbbildung?2 The precise nature of the generalization that Wittgensteinhere alludes to would appear to be somewhat of a mystery.In fact, an adequate account of this generalization is in the end

inseparable from an understanding of the Tractatus’ view of the natureand purpose of logical analysis, of how fundamentally this view di-verges from that of Frege and Russell. To gain such an understandingwill constitute the chief purpose of the present chapter. We can, how-ever, already begin to get a clearer idea of what is at stake in theintroduction of the notion of logical form if we first recall the ultimatepurpose of the picture theory – namely, to serve as a means of shed-ding light on the significant proposition. It then becomes apparent thatWittgenstein must somewhere address the obvious point that, as heputs it at 4.011, “at the first glance the proposition – say as it standsprinted on paper – does not seem to be a picture of the reality of whichit treats” (emphasis mine). The problem, in other words, is that, de-spite the detailed consideration of the nature of representation in the2.1s, it is not immediately evident exactly how the Tractatus’ remarksabout the picture are to be extended to language in general. Mysuggestion, then, following Dreben, is that the notion of logical formis meant to ease this transition. That is, by generalizing the idea ofform – by speaking not simply of what the picture must have incommon with reality to depict it “in its particular way” (seine Art undWeise; TLP 2.17), but also of what it shares with reality in order todepict it at all – Wittgenstein can hope to get us to think of picturingin cases in which no literal structural resemblance is involved.3 Thus,in reflecting on the thought or proposition as a “logical picture of thefact” (TLP 3), we will concern ourselves with the relation of pictureand pictured only with regard to the bare possibility of their beinglogically linked, a possibility that is presumably contained in the moretangible connection between, say, a spatial representation and thecorresponding fact.Now just how we are to conceive of such a “bare possibility” is, of

course, unclear. And indeed, although we might suppose the unclarityof this notion to be necessary, given the perspective the Tractatus


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ultimately aims to communicate, by the time of the Philosophical Re-marks Wittgenstein seems to doubt whether the generalization of thepicture can in any way be legitimately employed:4

It’s easy to understand that a ruler is and must be in the same space asthe object measured by it. But in what sense are words in the same spaceas an object whose length is described in words, or in the same space asa color, etc.? It sounds absurd. (PR 45)

Here the very possibility of the analogy between pictorial and logicalform is called into question. Nonetheless, even in this criticism we seewhat Wittgenstein implicitly regards as central in the Tractatus’ exten-sion of the notion of picturing. For in relying on the metaphor of theruler, he is once more bringing to the fore the application of a particularmethod of representation. As in the account of the ordinary picture,then, logical picturing would seem to be approached with an eye tosuch application, with an eye to how “reality” in the Tractarian senseof the term, is structured through our specific way of describing it. Theimportance of this point will become apparent as we seek to elaboratethe Tractatus’ development of the idea of logical form.

II

Many of Wittgenstein’s remarks about the proposition in the early 3sin fact closely parallel those about the picture. Thus, 3.14 – “Whatconstitutes a propositional sign is that in it its elements (the words)stand in a determinate relation to one another” – mirrors 2.14 inphasizing the facticity of the propositional sign. 3.141, in referring tothe propositional sign as “articulate” and as other than a mere “blendof words,” brings to the fore the distinction between a fact and a name,just as was suggested in 2.15 with regard to the difference betweenpicture and pictorial element. Indeed, the reliance on the earlier pointsabout the picture is quite explicit at 3.1431: “The essential nature ofthe propositional sign becomes very clear when we imagine it madeup of spatial objects (such as tables, chairs, books) instead of writtensigns. The mutual spatial position of these things then expresses thesense of the proposition.” In reflecting on the way the elements of aspatial picture are related to each other, it would seem that we aremeant to understand the essence of the proposition.

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Now certain details of the Tractatus’ view of the notion of sense willhave to await treatment in the next chapter. But already we are in aposition to approach the controversial and much discussed remark3.1432: “We must not say, ‘The complex sign “aRb” says “a stands inrelation R to b”’; but we must say, ‘That “a” stands in a certain relation(einer gewissen Beziehung) to “b” says that aRb’.” This remark is oftenheld to suggest something about Wittgenstein’s view of the unrealityof properties and relations.5 Thus, it is maintained, in a picture depict-ing a book lying on a table, the spatial relationship between the tableand the book is not itself part of the picture, but, instead, is shown bythe fact that these objects are related to each other in the way theyare. In the same way, the argument goes, in the proposition expressingsuch a fact it is the relation of the letter “a” representing the book tothe letter “b” representing the table that expresses the fact that aRb.“R” thus does not name anything; what it tries to represent is insteadshown by “a” and “b” bearing to each other a certain relation. Thethrust of 3.1432 is then to claim that relations (and, by extension,properties) are not objects and, thus, contrary to Russell, are to beregarded as in some sense unreal.One obvious problem for this whole line of interpretation is that, in

a previously cited remark in the Notebooks, Wittgenstein appears ex-plicitly to deny this claim: “Relations and properties, etc. are objects,too” (NB 61). Similarly, in a conversation about the Tractatus in 1930–31, he is quoted as saying: “ ‘Objects’ also include relations: a propo-sition is not two things connected by a relation. ‘Thing’ and ‘relation’are on the same level. The objects hang as it were in a chain” (CL120). Still, we need not conclude from this that 3.1432 is therefore anattempt to establish that relations and properties are, after all, constit-uents of the propositional fact.6 Rather, I suggest that the whole at-tempt to view this remark as centrally concerned, one way or theother, with the question of the nature of Russellian relations missesthe point. For, indeed, can we automatically assume that the Tractatus’notation is to be assimilated to Russell’s – that Wittgenstein holds the“R” in “aRb” to represent the sort of thing designated by “is lying on”in a sentence like “The book is lying on the table”? Close considerationof this remark in conjunction with its predecessor would seem tosuggest, in this context at least, that this is not the case.3.1431 asks us to reflect on the spatial relationships between tables,

books, and so on in a propositional sign composed of these elements.


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It is these mutual spatial relationships that are said to “express thesense” of the proposition. So, if we take a book lying on a table as adepiction of a pencil lying on a chair, it is the book’s position vis-a-visthe table that would express the sense of this picture-proposition; thissense, we can say, consists in a particular arrangement of pictorialelements against the background of space. The point, as in 2.15, isthus to bring out the self-sufficiency, as it were, of the picture’s sense:we are to see it is just that the pictorial elements stand to each otherin the particular way they do that allows the picture-proposition to beexpressive, to depict some definite arrangement of objects in theworld. Nothing further is involved – only the taking of these pictorialelements as a fact within space.But it cannot always be literal physical space – or not this alone –

that constitutes the background against which the elements in anarbitrary propositional sign aRb are able to depict, since not all picturesare spatial (as 2.182 makes clear).7 Instead, as we have suggested, inmoving to an explicit account of the proposition, we are involved ingeneralizing in a certain way the earlier remarks about the picture. Itwould seem, therefore, that as the expressiveness of the spatial picturetakes place against the backdrop of a spatial form, the expressivenessor sense of the logical picture should be understood against the back-drop of the logical form. We can then ask: how are we now to under-stand, in general, the connection amongst the elements of the logicalpicture, the proposition? It is, I suggest, just this question, the questionof the general nature of the propositional unity, not the issue of thereality or unreality of spatial, temporal, and other so-called materialrelations, which represents Wittgenstein’s actual concern here.8

His response will then be seen to parallel – and provide a furtherelaboration of – his remarks about the structure of the picture at 2.14-2.15. We “must not say” that the complex sign “aRb” says “a stands inrelation R to b,” because to do so would lead us toward a confusedunderstanding of the expressive power of the proposition. For in put-ting matters in this way, one seems to conceive of the proposition asessentially made up of a number of distinct elements that stand inneed of unification. We are then naturally brought to focus on theapparent special relation reflected in the propositional sign, to see it asthe key to the explanation of the proposition’s ability to have a sense.Thus we become tempted to posit the existence of something like a“logical form” to hold together the propositional elements, as in Rus-

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sell’s multiple relation theory,9 or to speak, as Frege does, of theinherent “unsaturatedness” of the function as making possible its com-bining with an object in the judgment.10

Wittgenstein seeks to eliminate these temptations at their root. Tosay along with the Tractatus “That ‘a’ stands in a certain relation to ‘b’says that aRb,” is not to replace one account of the nature of thepropositional unity with another, but rather to give up the wholeattempt to inquire into such a question. It is to see that the claim that,for example, the function sign is able to combine with a name becausefunctions have some special connection with objects puts the cartbefore the horse; instead, we are acknowledging, it is only becausethese constituents do combine to yield a significant proposition thatwe are able to draw the distinction between functions and objects inthe first place. Wittgenstein’s point, then, is that our entire hold onthe supposed relation between a and b in the assertion that aRb isparasitic on how we are able to operate with “a” and “b.” We can thussay no more of the unity characterizing the significant propositionthan that it consists in the particular way these elements hang togetherin the propositional sign.11 The relation R, on this view, is then merelyan internal feature of our notation, an outgrowth of the way we havedecided to preserve the propositional unity in our analysis; it corre-sponds to what might also be expressed in the use of different signsfor functions and objects, as when we write “f(a).”All of this is summed up for Wittgenstein by saying that a proposi-

tion must be distinguished from a name, as he maintains in the remarkfollowing 3.1432: “States of affairs (Sachlagen) can be described butnot named. (Names resemble points; propositions resemble arrows,they have sense)” (TLP 3.144). To suppose that a Sachlage could benamed is inevitably to be led into searching for some further element,something that must be added to the proposition in order for it to becapable of expressing that fact. In seeing the proposition as akin to anarrow, by contrast, we are acknowledging the intimate connectionbetween being a proposition and having a sense. An arrow does notconnect to the direction it specifies by means of some intermediary;rather, it is the specification of a direction. Similarly, the sense ofthe proposition – its “direction” – cannot be viewed as external to theproposition’s nature, but is instead constituitive of it: sensicality,we might say, is nothing other than the particular arrangement ofpropositional elements against the backdrop of logical space. Notice,


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however, that this whole account quite naturally opens up the ques-tion of the nature of this supposed “backdrop,” the possibility of theproposition. Thus, just as Wittgenstein’s discussion of the pictorial factwas seen to clear a space for an inquiry into the nature of the pictorialform, so here his inquiry turns to the nature of the logical form. Andas that earlier account centered around the essential or nonarbitrarydimension of the pictorial element, so at this point he is concerned toinvestigate what is essential in the name.

III

The Tractatus’ account of the name is bound up with the idea of acomplete analysis of the proposition: “In propositions thoughts can beso expressed that to the objects of the thoughts correspond the ele-ments of the propositional sign. These elements I call ‘simple signs’(einfache Zeichen) and the proposition ‘completely analyzed.’ The sim-ple signs employed in propositions are called names” (TLP 3.2–3.202).Among the many mysteries that the Tractatus presents, one has alwaysconcerned what an actual analysis into elementary propositions con-sisting only of names might look like; Wittgenstein notoriously neveroffers an example. That this omission is no mere accident on his part,but is instead a necessary consequence of his whole conception oflogical analysis, should be evident from 5.5571 alone: “If I cannot giveelementary propositions a priori then it must be obvious nonsense totry to give them.”12 Still, we may grant that it will be nonsense as faras Wittgenstein is concerned to give an example of a completely ana-lyzed proposition, while still inquiring into why the possibility of suchan analysis is thought to be so important. Through a consideration ofthis issue, we can gain an understanding of the Tractatus’ view of thename and the nature of logical form.The key to making sense of the Tractatus’ position in this regard lies

in a close consideration of 3.24, a remark that we began to discuss inthe previous chapter.13 Let us now quote this remark in its entirety:

A proposition about a complex stands in internal relation to the propo-sition about its constituent part.A complex can only be given by its description, and this will either beright or wrong. The proposition in which there is mention of a complex,if this does not exist, becomes not nonsense but simply false.That a propositional element signifies a complex can be seen from an

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indeterminateness in the propositions in which it occurs. We know thateverything is not yet determined by this proposition. (The notation forgenerality contains a prototype).The combination of the symbols of a complex in a simple symbol can beexpressed by a definition.

In our earlier discussion of this passage, we suggested that part ofWittgenstein’s concern here is to bring out the misleading nature ofthe notion of the complex. If our intuitive understanding of “complex”is of a term designating an entity having constituents or parts of somesort – and it is difficult to imagine what other sense could be given tothis notion – then it would seem that any analysis of a propositionmaking mention of a complex would proceed by way of a furtherdescription. But, as we saw, Wittgenstein points out that this is just tosay that whatever corresponds to the nonsimple propositional elementis, from the point of view of logic, not a genuine component of theworld, an object. Its complexity is not named, but is rather mademanifest through another proposition, or series of propositions; struc-ture is represented only by structure, as has been stressed in thepicture theory.In the first instance, then, reflection on the notion of analysis helps

to make sharp the distinction just drawn at 3.144 between the nameand the proposition. It now becomes clear that the components of theunanalyzed proposition should not be construed as names, simply byvirtue of their superficial appearance as the designators of entities. Atthe same time, though, this account leads us to wonder about howordinary language manages to function, to make contact with thesimple objects corresponding to the genuine names. It may seem as ifWittgenstein is committing himself to the claim that the sense of theunanalyzed proposition is somehow undetermined, that we thereforehave to wait on analysis, on logic to tell us what we really mean. Issuch a view not implied in the above assertion that the appearance ofthe complex is marked by an “indeterminateness” in the proposition?Certainly Russell reads Wittgenstein in this way, suggesting in theIntroduction that the Tractatus is concerned to lay down “conditionsfor a logically perfect language” and that ordinary language only hasmeaning “in proportion as it approaches to the ideal language whichwe postulate” (TLP, p. 8).But Wittgenstein explicitly disavows this conception in the Note-

books: “This is surely clear: the propositions which are the only ones


54

that humanity uses will have a sense just as they are and don’t waitupon a future analysis to acquire a sense” (NB 62).14 And, indeed, thissame idea is expressed in the above passage from the Tractatus. For insaying that the proposition about the constituent (i.e., the analyzingproposition) is “internally” related to the proposition about the com-plex, Wittgenstein would seem to be calling attention to the way inwhich logical analysis demands the preservation of sense, the way inwhich analysis could not be possible unless this were the case. Toillustrate, let us consider Russell’s way of handling nondenoting con-cepts in his Theory of Descriptions (an important example, given thatWittgenstein here and at 4.0031 seems to regard it as the paradigm ofanalysis). Whatever we are to say about the correctness of Russell’streatment of sentences like “The present king of France is not bald,”we must recognize that his suggested analysis can have a hope ofadmissibility only if we are willing to regard the analyzed expression –“�∃y (By & ∀x (Px ↔ x�y))” – as, in Quinean language, a paraphraseof at least some aspect of the unanalyzed. This whole enterprise wouldthus seem to depend on the original proposition already havingwhat Wittgenstein at 3.23 and 3.251 calls a “determinate” (Bestimmte)sense.On this account, a certain “indeterminateness” in the nonelemen-

tary proposition then serves as a means of allowing for the possibilityof its analysis – which is to say for the possibility of the definiteness ofits sense. This idea may seem to have an aura of paradox about it. ButWittgenstein’s point becomes clearer when we understand the impor-tant claim in the above passage that we know that everything has notbeen determined by the unanalyzed proposition. The suggestion herewould seem to be that the undeniable vagueness we find in the non-elementary proposition is in a certain sense circumscribed: just be-cause I can take into account the way in which my expression isimprecise it is able to function perfectly adequately in ordinary con-texts.Wittgenstein elaborates this further in the Notebooks:

If the complexity of an object is definitive of the sense of the proposition,then it must be portrayed in the proposition to the extent that it doesdetermine the sense. . . . For if I am talking about, e.g., this watch, andmean something complex by that and nothing depends upon the way itis compounded, then a generalization will make its appearance in the

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proposition and the fundamental forms of the generalization will becompletely determinate so far as they are given at all (NB 63–4).

Let us suppose that I assert that a watch is lying on the table and wishto infer from this that a wheel inside the watch is also lying on thetable. “The watch” here can be said to refer to something complex, inthat awareness of the referent’s composition is necessary for fullyunderstanding what I mean. But this is not to say that I must conducta complete investigation into the physical makeup of the watch beforeI can speak meaningfully about it. Central to the Tractatus is thethought that sensicality must be conceived as independent of the waythings happen to stand (see, e.g., TLP 4.061: “If one does not observethat propositions have a sense independent of the facts, one can easilybelieve that true and false are two relations between signs and thingssignified with equal rights.”). My claim about the watch then makesroom for that (apparent) object’s complexity without committing itself,as it were, to a full specification of its components; it is enough for thesense of this proposition for me to know of the thing lying on thetable simply that there is some mechanism inside of it. Definiteness ofsense would thus appear to be compatible with, indeed made possibleby, a certain indefiniteness in our ordinary propositions.We can now see why both 3.24 and the Notebooks passage above

speak of generality in connection with the nonelementary proposition.For the indeterminateness that marks the appearance of a complex isjust the arbitrariness that, from Wittgenstein’s perspective, is intrinsicto a generalization. The details of his view of generality will have toawait our discussion of the quantifier in the next chapter, but the keyidea is that “the watch” in the above nonelementary proposition isbeing treated in effect as a variable. We know that the features of theobject fall within a specified range of possibilities, but it is an indiffer-ent matter, as far as this proposition is concerned, as to preciselywhere; “the watch” plays the part of an arbitrary member of whatWittgenstein will call a series of forms.The role of analysis, it would then seem, is to specify in some

manner the particular members of that series, to individuate thatwhich is indicated in the unanalyzed proposition only en masse (i.e., asthe close of 3.24 suggests, as a combination of symbols linked to asimple symbol only via definition). 2.0201, the previously discussedcounterpart to 3.24, describes the process as follows: “Every statement


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about complexes can be analyzed (zerlegen) into a statement abouttheir constituent parts, and into those propositions which completelydescribe the complexes” (TLP 2.0201). This remark is, of course, quiteopaque, even by Tractarian standards. But given the above notedimportance of Russell’s Theory of Descriptions to Wittgenstein’s con-ception of analysis,15 we may suppose that the first part of this claimis envisioning something along these Russellian lines. That is, the“statement about [the] constituent parts” of the complex would in-volve a claim asserting the obtaining of a series of conditions – namely,all the categories or forms that would be necessary to describe thisstructure. Thus, if the watch in the above example could be completelycharacterized in terms of a description of the color (C) and shape (S)of its parts,16 then the analysis of the proposition asserting that thewatch is lying on the table – assuming that the phrase “lying on thetable” (L) could be understood as indicating a form – would begin withan existentially quantified statement of the form: “∃x(Cx&Sx&Lx).”The analysis would then be concluded – the statement about thecomplex would be resolved into those propositions in which thatcomplex is “completely described” – when we have produced a seriesof sentences in which the quantifier no longer appears. Logical analy-sis can thus serve to present, in an absolutely perspicuous form, thesense that belongs to the propositions of ordinary language.17

Still, it may well seem, on the basis of this account, that an analysisof this nature must ultimately involve a kind of empirical investiga-tion. For how would we determine what are the ultimate componentsof the watch (and hence what needed to be described by our analyzingpropositions) without opening up that watch and literally taking apartpiece by piece its internal mechanism? If Tractarian analysis indeeddoes entail such a process, however, it begins to seem as if sense can’tbe construed as independent of circumstances in the world. After all,given that I have not engaged in the appropriate investigation of thewatch, it would appear that I must remain ignorant of much that hasin fact been left open by the unanalyzed proposition in which a rep-resentative for this object appears. Hence I cannot be supposed to reallyunderstand my assertion “The watch is lying on the table” – such anunderstanding could only be had by a watchmaker or perhaps a phys-icist. And this is to say that analysis would then seem to be requiredto reveal the actual sense of the proposition – contrary to what we

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have suggested. Is this not the view to which Wittgenstein is ulti-mately committed?The Notebooks makes it quite apparent that this is not the case: “If,

e.g., I say that this watch is not in the drawer, there is absolutely noneed for it to FOLLOW LOGICALLY that a wheel which is in the watchis not in the drawer, for perhaps I had not the least knowledge thatthe wheel was in the watch, and hence could not have meant by ‘thiswatch’ the complex in which the wheel occurs” (NB 64–65). Similarly,he remarks several pages later: “It is clear that I know what I mean(meine) by the vague proposition” (NB 70). For Wittgenstein, it wouldseem, there can be no question of my attempting to mean somethingof which I am completely unaware.18 Tractarian analysis must insteadalways be understood as analysis of my sense, not of some idealized orunattainable sense.19 Its purpose will not be to eliminate the vaguenessof the unanalyzed proposition, but rather to characterize that vague-ness – or, better, to show that such vagueness poses no threat to theability of the ordinary sentence to express. Thus Wittgenstein com-ments in the Notebooks that his whole concern could be described asone of “justify[ing] the vagueness of ordinary sentences” (NB 70, em-phasis mine).Intrinsic to Wittgenstein’s approach, we might then say, is a distinc-

tion between the vagueness of a sentence and the determinateness ofits sense. Here he would seem implicitly to be moving against Fregeand a Fregean approach to analysis.20 Frege famously holds that aproper scientific concept is one that must be capable of deciding forevery object in the universe, whether or not it falls under that con-cept.21 A concept that does not have “sharp boundaries” in this senseis thought to be entirely meaningless.22 For Wittgenstein, though, thisis confusing a requirement for a more consistent application of signs –which indeed is important for genuine science – with a condition oftheir sense. The point can be brought out through consideration ofanother passage in the Notebooks:

I tell someone “The watch is lying on the table” and now he says: “Yes,but if the watch were in such-and-such a position would you still say itwas lying on the table?” And I should become uncertain. This shewsthat I did not know what I meant by “lying” in general. If someone wereto drive me into a corner in this way in order to shew that I did notknow what I meant, I should say: “I know what I mean; I mean just


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THIS,” pointing to the appropriate complex with my finger. And in thiscomplex I do actually have the two objects in a relation. (NB 70)

It is here admitted that I will not ordinarily be prepared to say of allpossible locations of the watch whether or not it can be said to belying on the table. But why should this be taken to imply that I didnot know what I meant in the first place? It is not as if, in uttering mysentence, I am attempting to perform a scientific experiment and it iscrucial to have something to say in every borderline case. Wittgensteinsuggests instead that what is necessary for my proposition to have adeterminate sense is only that it allows for some range of locations thatwill count as the watch’s lying on the table (and some range that willcount as its not doing so); for there to be something that I mean inthis instance the existence of a paradigm case is sufficient. Surely,though, this condition is satisfied by the sentence about the watch,and, moreover, in its general formulation, by any sentence we shouldordinarily count as meaningful. But then, on this account, all sensewould turn out to be determinate sense – which is really to say thatthe notion of an intrinsic vagueness to what I mean must be seen asincoherent.23

We can now begin to see more clearly the idea behind Wittgen-stein’s demand that analysis be final or complete, as at 3.25: “Thereis one and only one complete analysis of the proposition.” For, as 3.23suggests, such an analysis would seem to represent nothing but away of expressing the determinateness that characterizes the sense ofthe proposition: “The postulate of the possibility of the simple signs isthe postulate of the determinateness of sense” (emphasis mine). Thepoint, in other words, is this. If I mean anything at all by my utterance,I should be able to render this in a perspicuous form, in the mannerdiscussed above (that is, through a description of all the logicallyrelevant features of the elements in my proposition). The questionthen arises as to whether such a specification would be complete. Toanswer in the negative would seem to involve imagining that myassertion leaves something open intrinsically – as if I might later cometo discover what I had originally meant. Witttgenstein’s assertion of thedeterminateness of sense is then really equivalent to (what we haveseen to be) his dismissal of such a possibility as nonsense.24 Logicalanalysis must in principle always be completable.It is thus evident that the Tractatus’ principle of a complete analysis

cannot be taken as a self-standing thesis about the nature of language

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but, rather, is to be understood as a way of undermining the supposi-tion of an essential indeterminacy in the sense of a sentence. At thesame time, however, reflecting on this idea brings into sharper reliefthe proper aim of a philosophical inquiry. For what would it mean togive a complete analysis in the Tractarian sense? Analysis, as we haveseen, is a process of laying out in a perspicuous form exactly what Imean in uttering some particular sentence. It is, we might thereforesay, a matter of bringing to light the definitions implicit in the seeminglysimple signs of the nonelementary proposition, since 3.261 (in a man-ner similar to 3.24) holds: “Every defined sign signifies via those signsby which it is defined, and the definitions show the way” (TLP 3.261).This process of analysis will terminate when I have arrived at “primi-tive signs” (Urzeichen) that “cannot be analyzed further by any defini-tion” (TLP 3.26) – that is to say when I have a sentence containingonly genuine names. With the name we thus would appear to have asign that can be given no further explanation of how it signifies; it isin some sense in immediate contact with the world.25 In specifying thereal names, it seems we are then making transparent the inner possi-bilities common to the world and the sentences that depict it, thelogical core of reality. And that suggests that a complete analysis ofthe proposition will reveal nothing other than, on the one hand, thelinguistic analogue to the pictorial form (the logical form), on theother, the timeless, unchanging substance described at the opening ofthe Tractatus.The conditions that must be satisfied for a specification of substance

can now be given more precise articulation: what is required is theidentification of the referents or meanings (Bedeutungen) of the namesin the fully analyzed proposition. Such a specification would, it seems,bring us almost literally to see the determinateness, the logical ele-ments, that lie at the base of the significant proposition. Wittgensteinimplies something of this sort in this passage from the Prototractatus:

Although every word has meaning (bedeutet) via its definitions, this onlymeans that these definitions are necessary in order to present in oursign-language the full linguistic depiction of the thought to whose ex-pression the word contributes. But the definitions can be left tacitand the word does not then lose its meaning (seine Bedeutung), since itstill stands in the same relation to the objects which are depicted bymeans of the definitions – only we do not specifically depict that rela-tion. Naturally this often simplifies the sign-language and makes the


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understanding of it more and more difficult, because the decisive factornow lies outside the signs in something that is not expressed – theirrelation to their objects. (PT 3.202111)

A sharp contrast is here drawn between the purposes of logical analy-sis and those of ordinary human communication. While ordinarycommunication requires a certain simplicity of expression, logic seeksto articulate the full complexity of our language. Its aim in doing so isnot to provide the elements of the proposition with a Bedeutung – aswe have seen Wittgenstein’s fundamental thought is that logical anal-ysis cannot serve to “improve” our language in this way – but, rather,to lay bare the relation of the sign to that Bedeutung. The question ofhow the realization of this “decisive factor” is achieved by analysisthen becomes the question addressed by the 3.3s.

IV

Still, it is not at once apparent just why there is a question here. For ifthe Bedeutung is the object for which the name stands, as 3.203 appearsto state, and I have analyzed the proposition into names, what moreis there for me to say about that Bedeutung? If you ask me who is inthe room, and I tell you John, Mary, and Ivan, surely that reply wouldcount as sufficient (even if it were incorrect). We might then supposethat Wittgenstein’s ultimate point about the unsatisfiability of the log-ico-philosophical inquiry must depend on his later claim about theimpossibility of specifying the elementary propositions a priori – as ifthat inquiry’s goal would be realizable but for an unfortunate restric-tion on human analytical capacities.26 But I suggest that this is nothow his argument proceeds. Instead, the point of the upcoming re-marks is precisely to see why the attempt to specify the Bedeutungen isunlike my above example of listing the individuals in a room by name.Wittgenstein’s aim here, in other words, is to bring to the fore theessential ambiguity of the notion of a “logical object” – the very notionthat lies at the heart of the thought of Frege and Russell.Indeed, 3.3 has a distinctly Fregean ring to it, calling to mind his

famous “context principle” from the Foundations of Arithmetic. “Onlythe proposition has sense; only in the context of a proposition has aname meaning” (TLP 3.3). We might suppose that Wittgenstein is heremerely echoing what Ricketts has called Frege’s “judgment-centered

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metaphysics.”27 But while it is true that Wittgenstein is emphasizingthe primacy of the judgment, his way of developing this idea willassume a very un-Fregean cast. For what is the force of restricting theBedeutung of the name to the propositional context? Wittgenstein’sanswer is developed through the new notion of an expression (Aus-druck). “Every part of a proposition which characterizes its sense I callan expression (a symbol). (The proposition itself is an expression).Expressions are everything – essential for the sense of the proposition– that propositions can have in common with one another. An expres-sion characterizes a form and a content” (TLP 3.31). An expression isany part of a proposition that contributes to the sense of the whole.We can then only identify expressions by reference to the propositionsin which they occur; it is incoherent to suppose that they might occurin isolation. (The limiting case of this claim will be the one in whichthe expression is a proposition.) That, however, is not to suggest thatan expression is some sort of free-floating object that propositionallybound signs can alone latch on to successfully. Rather, the point isthat an expression is constituted by the occurrence of some sign or signswithin a certain set of propositions. It is, as 3.326 suggests, nothingbut the sign in its “significant use.”To grasp an expression will then entail the recognition of a “com-

mon characteristic mark of a class of propositions” (TLP 3.311). Itsappropriate presentation is by means of a variable in Wittgenstein’ssense, which is, on the face of it, a Russellian propositional function“whose values are the propositions which contain the expression”(TLP 3313). Thus, for example, one expression would be given byseeing what is common to the propositions “The cup is red,” “Thebook is red,” “The table is red,” and so on – that is to say by thepropositional function “x is red.” Now it is important to emphasizehere that the mere occurrence of the words “is red” does not by itselfensure that these sentences have something in common; again wemust pay attention to the way these signs contribute to the sense ofthe propositions in which they occur. Wittgenstein repeats this pointseveral times, for example, at 3.323: “In the proposition ‘Green isgreen’ – where the first word is a proper name and the last an adjec-tive – these words have not merely different meanings but they aredifferent symbols [expressions].” Similarly, although less obviously, hesuggests in a later conversation with Schlick, Waismann, and Carnapthat in the sentences “The table is brown” and “The surface of the


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table is brown” the phrase “is brown” constitutes two different expres-sions. After all, while in the first sentence “is heavy” can be meaning-fully substituted for “is brown,” in the second this yields nonsense.28

An expression can be given only through a consideration of all thepropositions in which some set of signs can occur.Now we can begin to become clearer on the import of Wittgen-

stein’s “context principle,” which is restated in a somewhat differentform at 3.314: “An expression only has meaning (Bedeutung) in aproposition. Every variable can be conceived as a propositional vari-able.” The context principle would seem to be somehow equivalentto, or explained by, the claim identifying all variables as propositionalvariables. This latter identification may at first seem surprising, as ifWittgenstein were denying the possibility of the predicate calculus.Clearly, however, such cannot be his intent. This remark must insteadbe understood as a way of making evident what is meant by “thecontext” in which the Bedeutung of an expression is to be considered.The proper presentation of an expression is, as we have seen, by wayof a variable. 3.314 is then emphasizing how the introduction of thevariable requires our already being given a class of propositions, howthe variable serves only as a kind of description of what those propo-sitions share logically. This indeed is stated more or less explicitly at3.316: “What values the variable can assume is determined. The deter-minations of the values is the variable.” We might say that the variableis ultimately nothing but a certain way of regarding a sign or sequenceof signs; it is the sign seen as logical mark of a class of propositions.29

Wittgenstein’s context principle then serves essentially to equate thislogical dimension of the sign with the Bedeutung of the expression. Weunderstand a meaning only when we look to how the propositionalsign functions within a whole class of propositions.With this idea in mind, we can make sense of Wittgenstein’s way of

introducing the notion of Bedeutung at 3.203: “The name means (be-deutet) the object. The object is its meaning (Bedeutung). (“A” is thesame sign as “A.”)” The natural inclination – one that is followed bymost Tractarian commentators – is to suppose that Wittgenstein is heresuggesting that “object” and “meaning” are simply interchangeable,and that the name therefore stands for a meaning in the same waythat a red patch might serve as a pictorial representative of a chair.But we saw earlier in our discussion of the picture theory that theTractatus uses the term vertreten to designate this arbitrary relation

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between a pictorial element and an object.30 And indeed this sameterm appears again at 3.22: “In the proposition the name is the repre-sentative of (vertritt) an object.” It appears, then, that the bedeutenrelation has to do not with the arbitrary aspect of the relation betweena sign and its referent, but, rather, with what Wittgenstein would callan “essential” feature – namely, the way the sign contributes to thesense of the proposition in which it occurs. It is to stress how graspingthis nonarbitrary dimension of the name entails considering its occur-rence in a whole class of propositions that Wittgenstein adds the par-enthetical remark about “A” being the same sign as “A.”31 Just as inthe first part of the picture theory, then, we see that two dimensionsof the relation between signs and reality are distinguished – and,correspondingly, just as in our discussion of the text’s opening re-marks, that two dimensions of the objects thereby depicted alsoemerge. (Note how 3.31’s reference to an expression characterizing a“form and content” echoes 2.025’s similar claim about substance.)What the name “means” is thus indeed the object, but the objectconsidered only with respect to its form.It now becomes clearer why the identification of the Bedeutung will

be of central importance in the Tractatus and, moreover, how such atask is tied in to the Fregean and Russellian projects. For if the mean-ings of the names are equated with the forms of objects, then, givenwhat we have said about the latter notion in the previous chapter, inspecifying those meanings we will have specified the fundamentalcategories of thought or language – that is to say, the logical forms.The endeavor to make evident such categories would seem to be whatRussell has in mind in the Principles of Mathematics when he speaks ofthe need for gaining a clear grasp of the “indefinables,” a task hepresents as “the chief part of philosophical logic.”32 In Frege’s thought,too, the concern with the fundamental logical categories is central,expressing itself in his distinction between functions and objects. But,then, given the connection between a specification of the meanings ofthe primitive signs and the more grandly metaphysical aims inherentin the remarks of the 1s and 2s, it would seem that Wittgenstein ishere bringing out the truly exalted nature of the Fregean and Russel-lian projects. That is, if the attempt to identify our basic logical cate-gories is really another way of getting at the fundamental connectionbetween language and the world, the unchanging substance that issomehow at the heart of both, then Wittgenstein would be showing


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that the work of these authors has even greater import than theymight have imagined. The Tractatus could then rightly be said to becompleting that work, bringing it to its inevitable conclusion.Of course, we have already seen in our discussion of the first part

of the picture theory that Wittgenstein’s “completion” of (what hetakes to be) the Frege/Russell project will entail a complete shift inour understanding of its nature. And, indeed, just such a shift beginsto become evident in this context in the remarks concerning Russell’stheory of types. “From this observation [about the nature of logicalsyntax] we get a further view – into Russell’s Theory of Types. Russell’serror is shown by the fact that in drawing up his symbolic rules he hasto speak about the meaning of the signs” (TLP 3.331). The theory oftypes is, of course, Russell’s attempt to avoid the class paradox – thecontradiction that ensues from assuming the class of all classes that donot contain themselves as members – and its analogues. In essence, itinvolves supposing a hierarchy of logical types of entities: at the bot-tom level individuals, then (according to the presentation in PrincipiaMathematica) propositional functions that apply to individuals, thenpropositional functions that apply to propositional functions that applyto individuals, and so on. The theory of types serves to restrict theapplication of the propositional function only to entities of the imme-diately preceding level and thereby allows us to avoid the paradoxes.Still, while the above remark makes it clear that the Tractatus re-

gards this approach as somehow illegitimate, it is not at once obviousjust what sort of “error” Russell is thought to have committed. Manycommentators suppose that Wittgenstein’s criticism is made in light ofa proposed technical alternative to the theory of types, one in whichno mention is made of the referents of the signs.33 Certainly, theallusion to “logical syntax” could well seem to support the view of theTractatus as arguing for a Hilbert-style, purely syntactical approach tologic:34 “In logical syntax the meaning (Bedeutung) of a sign oughtnever to play a role; it must admit of being established without men-tion being thereby made of the meaning of a sign; it ought to presup-pose only the description of the expressions” (TLP 3.33). Nonetheless,even without an understanding of the role of the term Bedeutung inthe Tractatus, it should be evident from the reference here to theprimacy of “description” of expressions that this passage, rather thanconstituting some new departure on Wittgenstein’s part, is simply a

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continuation of the above discussion of the variable, of the idea ofanalysis more generally. And that suggests that we should not viewhis talk of “logical syntax” as part of an attempt to advocate someparticular technical approach to the study of logic, any more than wecan suppose him to have provided specific guidelines as to how tocarry out a complete analysis.35 Instead, it would seem that Wittgen-stein is here and throughout concerned only to get us to reflect on theidea of analysis, on how in general an analysis is to be carried out.Such reflection, as we shall see, is meant to reveal not a slight defectin the Russellian approach to logic, but rather a fundamental confu-sion at its heart.I suggest, then, that the real nature of the Tractatus’ criticism of

Russell becomes clear when we view it in light of the above discussionof the context principle.36 For what is the theory of types ultimatelyseeking to accomplish? From Wittgenstein’s perspective, it must beunderstood as part of the attempt to complete the kind of analysisspoken of in the Tractatus – that is, as an effort to set forth the funda-mental logical categories. Russell is seen as claiming that, by drawingthe distinctions between individuals and propositional functions andbetween the different levels of propositional functions, he has speci-fied the logical forms underlying all thought and language. In thensuggesting that Russell must “speak about the meaning of the signs,”Wittgenstein is really saying that the theory of types is committed totreating the logical forms as if they might be named – that is, as if theyconstituted further constituents of the fact that could be specified inadvance. Now, to hold that this move is an error is not to seek toimpose some restriction on what such a theory can meaningfullyexpress – a meta-theory of types as it were.37 Rather, what Wittgen-stein is trying to bring out is how this involves a misconstrual of whatit would mean to complete the task of analysis; we are supposed torecognize that the referent of a name couldn’t be what we are lookingfor as the endpoint of our inquiry. After all, we have just seen that toarrive at the Bedeutung of an expression one must consider a wholeclass of propositions with regard to what they have in common anddetermine how that common element contributes to the sense of thesepropositions. One might then take a sentence like “The book is red” ascharacterizing an expression (recall from 3.31 that the propositionitself is an expression), but only when some subset of these signs is


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viewed in terms of its role in a particular class of propositions does itgive us a meaning. Again, a form is determined only by viewing somestring of signs as a logical mark.For Russell, though, it is almost the opposite. With the theory of

types, he seems to be imagining that our grasp on the significantsentence comes by way of a prior hold on the form. To believe thatwe could say that, for example, propositional functions ranging overindividuals constitute one logical type would appear to involve sup-posing that it is this variable that dictates to the propositions constitut-ing its domain – as if the logical form might represent a criterion ofsense. For Wittgenstein, Russell’s need to speak of what his signsmean bespeaks a tendency to attribute to logic just the wrong kind ofpriority.Indeed, we might say that Russell’s belief that there is even a need

for a theory of types is, from the Tractarian perspective, already anindication of a fundamental confusion. This is what is suggested in3.333:

A function cannot be its own argument, because the functional signalready contains the prototype of its own argument and it cannot con-tain itself. If, for example, we suppose that the function F(fx) could beits own argument, then there would be a proposition “F(F (fx))” and inthis the outer function F and the inner function F must have differentmeanings (Bedeutungen); for the inner has the form φ(fx), the outer theform �(φ(fx)). Common to both functions is only the letter “F,” which byitself signifies nothing. This is at once clear, if instead of “F(F(µ))” wewrite “(∃φ) : F(φµ). φµ � Fµ.” Herewith Russell’s paradox vanishes.

Wittgenstein’s point is that when we become clear on what it meansto treat a function sign as a variable rather than as a name, we recog-nize that, in a sense, there is no paradox with which to concernourselves. “F” here is a schematic rendering of a class of propositionsof a particular form; the meaning of “F” will then be determined bythe use of certain signs common to that class. In “F(F(fx)),” the first“F” and the second will therefore not have the same meaning, since,to use Russellian terminology, the first “F” ranges over propositionalfunctions of type n, while the second ranges over functions of type n� 1.38 The idea, in other words, is that the function (i.e., the variable)is constituted entirely by the logical role it plays and these functionsplay different roles, given the differences in the classes of propositionsthat they characterize. But then that is to say that it will be impossible

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to construct a (significant) expression of the form F(F), where the two“Fs” constitute the same type of propositional function. This is, ofcourse, just the restriction that the theory of types is trying to institute,but Wittgenstein wants to show how this restriction is there expressedin a misleading way. For it is not, as the theory of types would suggest,because the two “Fs” in F(Fx) are of the same type that this expressionyields nonsense. Rather, it is just because the expression yields non-sense that we say these “F’s” are of the same type. One is remindedhere of 3.1432 (“We must not say, ‘The complex sign “aRb” says “astands in relation R to b’ ”; but we must say, ‘That “a” stands in acertain relation to “b” says that aRb’.”): Wittgenstein’s aim is once moreto bring out how our hold on a notion of logical form is parasitic onhow we speak, on what it makes sense to say. To recognize this is toacknowledge that a theory of types is unnecessary, if by that we areimagining some a priori restriction on what is permissible logically.Rather than seeking to “solve” “a paradox,” our focus instead shouldbe on gaining a clear understanding of the workings of our language.With such an understanding, we will be no more tempted to speak of“the class of all classes that are not self-members” than we would toask about the weight of a noise.39 Thus Wittgenstein adds at 3.334:“The rules of logical syntax must follow of themselves, if we onlyknow how every single sign signifies” (TLP 3.334).

V

But if it is now more apparent why the theory of types is dismissed asmisleading, we still have to become clearer on the nature of thealternative being proposed by the Tractatus. How will the meaning ofa sign or set of signs be expressed in what Wittgenstein would consideran appropriately constructed language? From the above discussion, itis certainly evident that such a language will not include any namesfor Bedeutungen; that, however, does not alone tell us how a Tractariananalysis of a proposition is to proceed. Let us then use as our example“The watch is lying on the table.” In our analysis, as we have seen, wewill be concerned to make perspicuous what is needed for this propo-sition to express its sense. In this case, what will be required is, say, acolor dimension, as well as a position dimension. A thorough charac-terization of what I mean by “watch” and “lying on the table” will, ofcourse, require other dimensions as well, the full enumeration of


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which will only be given with the completion of the analysis. Butsuppose that color and spatial position are in fact among the dimen-sions, the forms that will be needed in the complete analysis; these, inother words, are two of the meanings involved in the above sentenceexpressing its sense.40 Suppose, further, that I choose to express theanalyzed sentence by means of a coordinate system (Wittgenstein infact speaks of such a system at TLP 3.41 and in a number of places inthe Notebooks41): one set of x- and y-axes will be marked off in units ofmeasurement, another set of axes perhaps in units of color and bright-ness. I will then express the claim that some position on the table hassome particular shade of color as, for example, the ordered pair�3,2�conjoined with an ordered pair representing a location on the color/brightness scales.Now what is central to notice here is that this specification makes

no mention of either position or color – the names in this languagerefer only to specific points within the coordinate system. And, indeed,as long as the scale of my coordinate system is well chosen initially Iwill be able to describe the color of any position on the surface of thetable in the same manner, simply checking off, as it were, the appro-priate points on my scale. The forms of color and spatial position arethus absorbed into my method of representation; they become part ofthe means by which I can describe the world rather than furtherelements that themselves have linguistic representatives. In the com-plete analysis of the above sentence, all Bedeutungen will similarlyvanish into the particular system in terms of which reality is to bedepicted.Reflection on the notion of analysis thus makes evident how I

might give a thorough description of the world without ever needingto have names of meanings, of logical forms. One is naturally re-minded here of Frege’s aforementioned concept “horse” problem42 andhis idea that the “ordinary language” distinction between conceptsand objects will ultimately express itself only in the use of the signs ofa canonical notation. Still, if Wittgenstein is simply following andextending Frege’s insight,43 then the objection that we might bringagainst the latter also would seem applicable to the Tractatus. For onemight want to ask Frege just why his Begriffsschrift is supposed to becriterial with regard to the concept “horse” problem. Why does thefact that the Fregean concept-script does not allow us to treat conceptsas objects show that it is a “confusion” to attempt to make this equa-

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tion in ordinary language, as Benno Kerry does? In the same way,then, one could seemingly ask Wittgenstein why the possibility of acertain kind of analysis demonstrates that Bedeutungen “really” cannotbe named. Indeed, we seemingly have to speak of the logical forms ininitially setting up the coordinate systems. For what reason are we todismiss such talk as “nonsense”?These objections fail to take into account the dialectical nature of

the Tractatus; we might say, then, that they serve only to bring out thedifference between Wittgenstein’s thought and Frege’s.44 For Wittgen-stein, far from being committed to supposing that the analyzed sen-tence constitutes the “correct” form of expression, is in fact concernedto suggest the nonsensicality of such a notion. His whole position in theTractatus (and in the later philosophy as well) rests on the assumptionthat we can make perfect sense with the language we already have:analysis, as we have suggested, is discussed not in order to correctsupposed deficiencies in our ability to speak and communicate, butrather only for the purpose of making clear the nature of the logicalinvestigation itself. As far as Wittgenstein is concerned, then, we canin “colloquial language” speak of “color,” “spatial position,” and so on,or refrain from doing so – nothing whatsoever is here at stake. It isonly if our aim is to identify the fundamental logical categories of ourlanguage (i.e., if we are engaged in philosophy) that his distinctionsbetween what can be spoken of and what cannot come into play.45 Inthis case, then, in reflecting on the absorption of the logical forms intothe particular coordinate systems that we set up, what we are meantto see is how everything we (as philosophers) would properly belooking for is built into the way we will speak. And that is just to saythat it must be nonsense to seek to specify the object of our search inadvance (and remember that for Wittgenstein it is only in such an apriori manner that a logico-philosophical inquiry is to be conducted).For although the specification of some position in, say, color spaceonly makes sense against the background of a particular coordinatesystem, that coordinate system itself is defined by the range of sig-nificant “color propositions.” This becomes particularly evident whenwe reflect on how we would determine whether or not such a sys-tem is adequate. Wittgenstein will later say that it is a matter ofthe set of signs having the right “logical/mathematical multiplicity”(see 4.04–4.0411, 5.475), but that simply means that it allows us toexpress all and only what we want to express – that is, that with


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this system we never expect to end up either at a loss for words,as it were, or depicting an impossible state of affairs.46 Notice, how-ever, that, were either such eventuality to take place, we would re-ject this representational system (and not our ordinary standards ofintelligibility) as inadequate.47 Criterial in logical analysis is what wecan meaningfully say and it is on this that we necessarily remaindependent.48

Wittgenstein’s whole point here is then really summed up at 3.327:“The sign determines a logical form only together with its logical-syntactical application.” It is, in other words, through the significantuse of the propositional sign alone that the logical form, the Bedeutungof an expression will emerge.49 This, in turn, brings us back to thecentral point of the picture theory. For this notion of the emergenceof the logical form through the proposition’s application mirrors pre-cisely the way we have seen the pictorial form, the inner possibilitiescommon to the picture and reality, to be structured through the pro-jection of the picture on to reality. And just as this latter idea ledWittgenstein to hold that the pictorial form can only be shown, so wesee here a clear anticipation of 4.121: “Propositions cannot representthe logical form: this mirrors itself in the propositions. That whichmirrors itself in language, language cannot represent. That which ex-presses itself in language, we cannot express by language. The proposi-tions show the logical form of reality. They exhibit it.” This remark,together with Wittgenstein’s subsequent insistence that that which“can be shown cannot be said” (TLP 4.1212), is standardly taken as oneof the clearest indications that the Tractatus is committed to the sup-position of deep, but inexpressible features of reality. But our discus-sion of the 3s should make plain how this interpretation of the show/say distinction is no more appropriate here than in the context of thepicture theory. For instead of flatly asserting the existence of an inef-fable domain of form, Wittgenstein is to be regarded as again attempt-ing to make evident the nature of the logico-philosophical inquiryitself. To hold that logical form is only shown is to emphasize how thewhole of the philosopher’s apparent subject matter is inextricably builtinto the coordinate system that allows us to express, that it makes nosense to look for it. A complete analysis into elementary propositionsconsisting only of names will make perspicuous how this is the case,not by allowing us to “better understand” logical form (whatever that

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would mean), but by removing the temptation to imagine that thereis anything to be understood in the first place.This point about the inherent unsatisfiablility of the philosophical

endeavor is further brought out at 3.3421:

A particular method of symbolizing may be unimportant, but it is alwaysimportant that this is a possible method of symbolizing. And this happensas a rule in philosophy: The single thing proves over and over again tobe unimportant, but the possibility of every single thing reveals some-thing about the nature of the world. (TLP 3.3421)

Here Wittgenstein is asking us to reflect on what it means to seek alogical or philosophical result. It seems to go almost without sayingthat a logical inquiry can terminate only when it has seized on thecorrect formulation of its subject matter, when it has in some sensecaptured the object of its search. This assumption finds expression inFrege’s very need to construct his Begriffsschrift, the presumed canon-ical presentation of the logic of our language. Wittgenstein’s claim thatit is only the possibility of a particular symbolism that reveals somethingabout the essence of the world is then meant to emphasize the emp-tiness of the attempt to specify that essence. For if, as he has suggested,the logical dimension of the sign of any language only emerges in theway that sign is applied, that aspect must be, so to speak, spread outacross a class of propositions: logic is not located at some single pointin a system of signs, but is made manifest by the language as a whole.There is then in a sense nothing for us to do to specify a logical form,nothing but to pay attention to the way the sign functions in the(significant) sentences in which it figures.This of course does not preclude the attempt to develop a special

notation, nor even deny that doing so might be helpful in certainways. As Wittgenstein puts it:

We can, for example, express what is common to all notations for thetruth functions as follows: It is common to them that they all, forexample, can be replaced by the notations of “�p” (“not p”) and “pvq”(“p or q”). (Herewith is indicated the way in which a special possiblenotation can give us general information). (TLP 3.3441)

Certainly, then, it is permissible, as far as Wittgenstein is concerned,to use what is in this case Russellian notation for the truth functions.


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But to say that this is a “possible notation” or that this constitutes amode of expression which might “replace” other means of expressingthe truth functions is to suggest that the notation does not give us byitself the inner logic of our language. In order to see the Russelliantruth functional notation as revealing something of the “essence” ofthe world we must take these signs together with all other notationsthat can express the same sense. We must, in other words, see thesesigns as characterizing an expression in the Tractarian sense of the term.But that makes evident that there is nothing logically privileged aboutthe Russellian notation, that these signs stand on the same level asany other in the class that they serve to characterize.Again, then, it becomes apparent how the inquiry into the logical

forms turns back on itself: what begins as an attempt to specify thenecessary features of the world ends with the recognition that theseextend as far as our language itself, that the “specification” can be nomore than an acknowledgment that we speak, sometimes with sense,sometimes nonsensically. This is just the thrust of 3.341 and 3.3411,which might be taken as the culmination of the discussion of the 3s.After drawing the distinction between accidental and essential featuresof the proposition, Wittgenstein states:

The essential in a proposition is therefore that which is common to allpropositions which can express the same sense. And in the same way ingeneral the essential in a symbol is that which all symbols which canfulfill the same purpose have in common. One could therefore say thereal name is that which all symbols, which signify an object, have incommon. It would then follow, step by step, that no sort of compositionwas essential for a name. (TLP 3.341 and 3.3411)

This notion of the “essential” in a symbol or expression is just anotherway of speaking of its Bedeutung. To hold that this essential aspect isarrived at by seeing what all symbols that can fulfill the same purposehave in common is thus really to reiterate how the logical form isspread out across a whole class of propositions. But then that is tosuggest that the “real name” that logic seeks is ultimately no name atall: its “composition” disintegrates precisely because what it refers to isnot a thing, in any ordinary sense of the term but an internal featureof our own language.This in turn brings out more fully the inherent ambiguity of the

notion at the center of the whole logico-philosophical inquiry, the

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notion of a logical object.50 It is not that Wittgenstein wishes to flatlydeny the existence of such entities, to hold that they are pure fictions.His aim instead is to get us to see how their “existence” rests on theexistence of objects as the arbitrary (or accidental) referents of namesin the sensical proposition. The logical object is not a thing, but, wemight say, a way of regarding the components of our genuine propo-sitions; it is the propositional constituent viewed in a special light. Thissection of the Tractatus intends to show precisely the fragility of such aperspective.

VI

Given this way of understanding the discussion of analysis in the 3s,Wittgenstein’s blunt characterization of the notion of an object as a“pseudo-concept” at 4.1272 should come as no surprise. Indeed, itquickly becomes apparent how the distinction between formal con-cepts/properties/relations and proper concepts/properties/relations isreally a kind of paraphrase of the points that have emerged in thepassages we have been considering. Thus, we find first at 4.122: “Wecan speak in a certain sense of formal properties of objects and atomicfacts, or of properties of the structures of facts, and in the same senseof formal relations and relations of structures.” In what sense can wespeak of such formal properties and relations? Wittgenstein makesclear in 4.122 that the term “internal” can be substituted for “formal”in these contexts. An internal property, however, is one that “it isunthinkable that its object . . . not possess” (TLP 4.123): two shades ofblue, for example, stand in the internal relation of brighter and darkerin that standing in that relation is constitutive of what they are; toremove these “objects” from that relation is “unthinkable” just becausewe can have no independent handle on their identity.51 But then itwould seem that we can “speak of” formal properties and relationsonly in the sense that we can utter propositions in which they figureas internal features. Thus, we might say that white should be added tothat magenta paint if the latter is to approach sky blue or remark onhow, at sunset, the sky has deepened to become magenta. By contrast,we (assuming we were fluent speakers of English) would not remarkon the magenta color of the sunset and then go on to wonder if thesky were darker than its ordinary color. That magenta is darker thansky blue is, it would seem, built into the statements in which these


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words can meaningfully occur – which is to say that what we wouldwant to express by this string of signs is shown by the existence of acertain class of propositions.This in fact is what Wittgenstein proceeds to assert about internal

properties and relations generally: “The holding of such internal prop-erties and relations cannot, however, be asserted by propositions, butit shows itself in the propositions which represent the facts and treatof the objects in question” (TLP 4.122). We can then say, to use theterms of our above discussion, that the internal or formal features of aconcept like “magenta” is properly presented by a propositional vari-able (or, perhaps, a number of propositional variables), whose valuesdefine the meaning of this notion. An expression like “magenta isdarker than sky blue” will be absent from the resulting class – will benonsense – just because it attempts, we might say, to assert a variable;it supposes that what is common to a number of propositions existsalongside those propositions, as a further fact to be represented. Inattempting to state a formal relation or property, it is thus as if wewere imagining that a triangle formed from the intersection of threelines might somehow be viewed apart from these (mere contingent)borders. Wittgenstein’s purpose would then be to expose the incoher-ence of this fantasy of getting at the triangle itself, to get us to see thateverything we are really after here emerges simply through a descrip-tion of the boundary lines that characterize this figure.Wittgenstein’s remarks about “formal concepts” express much the

same point:

In the sense in which we speak of formal properties we can now speakalso of formal concepts. . . . That anything falls under a formal conceptas an object belonging to it, cannot be expressed by a proposition. But itis shown in the symbol for the object itself. (The name shows that itsignifies an object, the numerical sign that it signifies a number, etc.)Formal concepts cannot, like proper concepts, be represented by a func-tion. For their characteristics, the formal properties, are not expressedby the functions. The expression of a formal property is a feature (Zug)of certain symbols. The sign that signifies the characteristics of a formalconcept is, therefore, a characterisic feature of all symbols, whose mean-ings fall under the concept. The expression of the formal concept istherefore a propositional variable in which only this characteristicfeature is constant. (TLP 4.126)

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We must first notice the position that the formal concept occupieswithin the overall Tractarian framework. Wittgenstein says that sucha concept is a feature of certain symbols – that is, an expression ofwhat these symbols have in common. But recall that the symbol(expression) is itself a way of characterizing a form, that which iscommon to a class of propositions. In speaking of a formal conceptWittgenstein has thus ascended a level from his earlier talk of theproposititional variable; the proper means of expressing a formal con-cept will then presumably be through what he calls a “formal series” –that is, a whole system of symbols (such as the one characterizing theconcept of being a successor) “ordered by internal relations” (TLP4.1252). Nonetheless, Wittgenstein suggests that a formal concept is,just like an expression or symbol, presented by way of a propositionalvariable. He can then be said to recognize in this sense no type distinc-tions with regard to variables: the formal concept is spoken of inexactly the same terms as the expressions it serves to characterize.52

(For this reason Wittgenstein asserts at 4.1271: “Every variable is thesign of a formal concept.”) By contrast, though, there remains anessential difference between the propositional variable and its values.Thus, Wittgenstein suggests that the formal concept, as part of whatsome number of symbols are, cannot (meaningfully) be set downalongside the propositions that this concept ultimately serves to char-acterize, as if they all stood on the same level. Or, to shift to theprevious metaphor, we could say that a formal concept like “object”must be conceived as part of the coordinate system that allows us toexpress, rather than constituting some determinate position withinthat framework. It will then be nonsense to attempt to make assertionsabout such notions.4.1272, the first bald assertion of the nonsensicality of the central

notions of Russellian and Fregean logic53 – as well as those that theTractatus itself has relied on – thus follows quite naturally from theprevious remarks:

So the variable name “x” is the proper sign of the pseudo-concept object.Wherever the word “object” (“thing,” “entity,” etc.) is rightly used, it isexpressed in logical symbolism by the variable name. For example inthe proposition “there are two objects which . . .” by “(∃x, y) . . .”.Wherever it is used otherwise, i.e., as a proper concept word, there arise


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nonsensical (unsinnige) pseudo-propositions. So one cannot, e.g., say“There are objects” as one says “There are books.” Nor “There are 100objects” or “There are �0 objects.” The same holds of the words “Com-plex,” “Fact,” “Function,” “Number,” etc. They all signify formal con-cepts and are presented in logical symbolism by variables, not by func-tions or classes (as Frege and Russell thought). Expressions like “1 is anumber,” “there is only one number nought,” and all like them arenonsensical. (It is as nonsensical to say “there is only one 1” as it wouldbe to say: 2 � 2 is at 3 o’clock equal to 4).

“Object,” “fact,” “function,” “complex,” “number,” and so on are allformal concepts in the above sense and consequently will not figurein any genuine propositions. Still, despite the preparation we havereceived for these claims, they are apt to be experienced as too quick.For we might well be inclined to ask: even if Wittgenstein has revealed“object” to be a formal and, therefore, mere pseudo-, concept, howhas this been shown of these other central notions? Do we not requirefurther arguments before this much more general conclusion can beproperly drawn?We do, of course, find further discussion of the notion of number

in particular in the 6s and to that extent these questions are appropri-ate. But in a more important sense, I would suggest that they miss themark entirely. For such questions reflect what we have seen to be afundamental assumption (whether explicit or implicit) of many Trac-tarian interpreters – namely, that Wittgenstein is throughout the textattempting to provide arguments for controversial and disputable the-ses. Even for those commentators who nominally reject this reading,who see the Tractatus as concerned solely to eliminate philosophicalconfusions, the tendency is quite strong at these points to attribute toWittgenstein something like a substantive doctrine. After all, if hisultimate aim really is to show the meaninglessness of all philosophicalquestions, he must be, as it were, laying his cards on the table whenhe comes out and says this (or something quite near to it). It is quitetempting to suppose that these sorts of utterances must occupy aspecial position in the framework of the Tractatus, to have a uniquestatus.54

But temptations only lead us astray in Wittgenstein’s austere worldand so must be countered. The temptation here is to imagine that“being a formal concept” is put forth as a criterion of nonsensicality, acriterion, we then go on to protest, which has not yet been shown to

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apply to “fact,” “number,” and so forth. But we must ask ourselveswhether this as a criterion has been shown to “apply” even to thenotion of an object. That is, is Wittgenstein’s method to make clearwhat an object is and then subsequently to go on to bring out howthat concept is, after all, only formal? Our whole discussion thus farhas been designed to suggest how this description is not adequate. Wehave sought to bring out that an understanding of the role of “object”in the Tractatus is its recognition as purely formal, that the only philo-sophical hold we have on this notion is as an intrinsic feature of ourway of representing the world. This recognition, in turn, is just therecognition of the nonsensicality (in the Tractatus’ sense of the term)of the attempt to provide a specification of the object. We might thensay that the claim “It is nonsense to seek to represent an object”constitutes, to use the language of the later Wittgenstein, a purelygrammatical remark. (In Tractarian terms we could say that it is anexpression of an internal relation.) The point, in other words, is thatour notions of object, formal concept, and philosophical nonsense areall given together, emerging through reflection on the pictorial natureof the proposition and what it would mean to provide an analysis.There can then be no question of offering criteria of nonsensicality, ofadopting a standpoint from which we can, once and for all, assess the“real character” of our utterances about objects.By contrast, however, the Tractatus’ reflection on the nature of the

proposition may lead us to understand differently the role of theobject; it may bring us to see, as I have suggested above, that the(philosophical) questions we were originally inclined to ask in connec-tion with this notion have lost their allure. Rather than establishingthe truth of certain propositions, the task of the Tractatus at this junc-ture could then be described as one of characterizing the philosophicalinquiry into objects so thoroughly that it crumbles under its ownweight. We do not thereby explain the philosophical perspective orreveal its true nature, but we can come to recognize its precariousness:we see through the terms of the Tractatus. These terms, moreover, areall of a piece; they are intended to characterize, as I have claimed, asingle viewpoint.55 And that means that the insight into the status ofone of the central Tractarian notions must be at the same time aninsight into the rest. In acknowledging the weakness of our grasp on“object” we are acknowledging the same about “complex,” “fact,”“function,” “number,” and so on.


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This point becomes even more evident when we notice the phrase“and so on” that follows this list of central notions – the list as Witt-genstein gives it at 4.1272. He plainly is not attempting to provide acomplete inventory of formal concepts, to go through all of our mis-leading notions one by one. Indeed, it would be nonsensical to attemptto do so a priori, since the logical forms are said to be “anumerical”(TLP 4.128). Rather, we are meant to see that the same kind of moveis described in the attempt to inquire into any of these notions, thatwe are in every case involved in imagining an incoherent detachmentfrom the fabric of our own language. The “and so on,” we might say,thus expresses the comprehensiveness of the shift in outlook that theTractatus aims to effect. We do not by means of this text arrive at new,superior accounts of “fact,” “object,” and “number.” What the Tractatusseeks instead is to lead us to regard in a new way our attempts togain clarity about all such notions; it seeks to get us to go on differentlyin our efforts to know the world. We are called to go on withoutphilosophy.

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C H A P T E R I I I

THE ESSENCE OF THE PROPOSITION

I

Wittgenstein’s attempt to undermine what he sees as the heart of thephilosophical endeavor would seem to be already well under way withthe completion of his initial account of analysis. It is not, then, thatthe straightforward attacks on the central notions of logic at 4.1272,4.1274, and 4.128 – or even his later 6.54 denial of significance to allof his own propositions – represent a sudden shift in the direction ofthe Tractatus. Instead, we have seen that these remarks should beunderstood as more explicit statements of what is Wittgenstein’s fun-damental point throughout – or, perhaps better, as indications of howwe are to regard the seemingly more metaphysical claims in the earliersections of the text. If we accept such an interpretation, however, onemight well wonder what work is left to be done after the 3s and early4s. Would not the central steps toward finding “on all essential points,the final solution of the problems” (TLP Preface) of philosophy alreadyhave been taken, a third of the way through the Tractatus?What, then,is the purpose of the rest of the book? Moreover, one might alsowonder how the account that we have given squares with Wittgen-stein’s subsequent concern to specify the “general form of the propo-sition” and his claim at 5.471 and 5.4711 that this specification repre-sents the essence of the proposition and, indeed, of the world. Wouldsuch ideas not imply that the real focus of “logic” is yet to be ex-pounded, that the account up to this juncture is in some sense onlypreliminary?We must recall once more the nature of the investigation in which

the Tractatus is involved. I have suggested that it aims to communicate


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a single view of the nature of logic, that indeed central to understand-ing the text (as well as the real character of its subsequent repudiationby Wittgenstein) is appreciating how it is committed to supposing akind of essence to the perspective it expresses. For Wittgenstein, then,it seems we should say that the Tractatus’ ultimate point can be graspedin its entirety at any juncture of the text. Thus, in a sense, there canbe no “preliminary” stages for us to pass through, no overwhelmingneed to go on once we appear to have grasped its central teaching.The absence of any further work to be done at this stage is then not acriticism but rather just the point.Nonetheless, the Tractatus does continue. This continuation, more-

over, is not in any obvious sense a mere repetition of the themesdeveloped in the first part of the text, but instead involves a host ofnew terms and seemingly new questions, as well as the introductionof various apparent technical moves. If the Tractatus is to be seen assetting forth a single unified vision, it is one that evidently requires agood deal of structure to be maintained.1 Our aim in this chapter is tomake as clear as possible the features the 4s, 5s, and 6s add to thatincreasingly complex structure – the analysis of the logical constants,the truth tables and the idea of logic as tautologous, the specificationof the general form of the proposition, and so on. But this “makingclear” must involve showing how these details can be regarded as partonly of an extension of a perspective, rather than the introduction of afresh set of principles. Our central purpose, in other words, will be toelaborate Wittgenstein’s further working out of the “problems of phi-losophy,” while at the same time preserving the sense of the wholeendeavor as the expression of a single thought.

II

To set the stage for the discussion that we find in these later sectionsof the book, we must first return to the initial account of the picture.After reiterating at 2.2 the identity of form between the picture andwhat it depicts, the next several remarks all deal with a picture’s“representing” of a “possibility” of facts:

The picture depicts reality by representing (darstellt) a possibility of theexistence and nonexistence of atomic facts. (TLP 2.201)The picture represents a possible state of affairs (Sachlage) in logicalspace. (TLP 2.202)

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The picture contains the possibility of the state of affairs it represents.(TLP 2.2.03)

Note first the parallel between these remarks – especially 2.201 – and2.11: “The picture presents (vorstellt) the states of affairs in logicalspace, the existence and nonexistence of atomic facts.” It would seemthat a picture “presents” existent and nonexistent atomic facts, but“represents” a possibility of such facts. Now I have already suggested2

that what a picture presents is all those states of affairs it can be usedto depict; a picture presents both existent and nonexistent facts be-cause the same picture that allows us to say that some fact A is thecase also allows us to say that A is not the case. What a picturerepresents would then seem to be the choice that is made among thesefacts laid out in logical space; it is, as it were, a possibility drawn fromthe set.3

An example will help to make evident the significance of this dis-tinction between the presenting and representing dimensions of thepicture. Let us take the case of a picture depicting a book lying on atable. If we correlate the pictorial book with a real book and thepictorial table with a real table, this picture will be said to “present”both the fact that the book is on the table and the fact that it is not onthe table. It “represents,” by contrast, some particular state of affairsin logical space, that is to say either the book’s lying on the table orit’s not doing so (but not both at once). We then ask: what determineswhich one of these possible states of affairs is in fact represented bythe picture in some given case? Wittgenstein develops his answer tothis question at some length in the Notebooks, as, for example, in thesepassages from November 1914:

The picture has whatever relation to reality it does have. And the pointis how it is supposed to represent (darstellen).4 The same picture willagree or fail to agree with reality according to how it is supposed torepresent. (NB 23) The method of portrayal (Abbildungsmethode; methodof depicting) must be completely determinate before we can comparereality with the proposition at all in order to see whether it is true orfalse. The method of comparison must be given me before I can makethe comparison. (NB 23)

The point in these passages seems to be that the possibility of a pic-ture’s representing some particular state of affairs – and hence itscapacity to be true or false – is dependent on the way that picture is as


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a whole compared with reality: it is just our method of comparisonthat decides whether we understand this picture as holding the bookto be on the table or not on the table. And, in the same way, it is themethod of comparison that determines whether a more complex pic-ture depicting, say, states of affairs A and B represents A v B, A & �B,�A � B, or any other truth functional combination. With the focuson the representational capacities of the picture, the so-called logicalconstants thus come to the fore. They are to be construed as thecharacteristic means of, as Wittgenstein puts it in the Notebooks, “pro-ject[ing] the picture of the elementary proposition on to reality” (NB29).It is important to see how, according to this story, the possibility of

applying any one of the logical constants might be said to presupposethe ability to apply all the rest. For the picture represents always aselection within the field of what it presents, as one might put it.Wittgenstein then attempts to bring out the sense in which that “field”is present in its entirety as soon as we have a picture of the world.This is what he has in mind, for example, at 3.42: “Although a prop-osition may only determine one place in logical space, the wholelogical space must already be given by it. (Otherwise denial, the logicalsum, the logical product, etc., would always introduce new elements –in co-ordination).” Part of the reason for this claim we have alreadyalluded to in our brief discussion of negation.5 For in pointing out thata picture of some fact A can be used to assert �A, we are really sayingthat both facts are given together: if we know what it means for thebook to be on the table we at the same time know what it is for it notto be on the table. That negative fact, moreover, is not some brutegesture toward the totality of things not identical with books on tables,as if we were supposing that the negation of A includes, besides �A,also B, C, D and so forth. Instead, the denied picture carves out adistinct state of affairs, occupying its own position in logical space. Thiswhole idea is perhaps stated most clearly and succinctly at 4.0641:

One could say, the denial is already related to the logical place deter-mined by the proposition that is denied. The denying proposition deter-mines a logical place other than does the proposition denied. The deny-ing proposition determines a logical place, with the help of theproposition denied, by saying that it lies outside the latter place. Thatone can deny again the denied proposition, shows that what is deniedis already a proposition and not merely the preliminary to a proposition.


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Now although there is one sign for negation in the language, say,of Principia Mathematica, we should not be misled by this into suppos-ing that “�p” specifies a unique way of comparing the propositionwith reality. For, as Wittgenstein later points out, “��p” will repre-sent this same fact, as will “�p v �p,” “p� �p,” and so on: “Thatwhich denies in “�p” is however not “�,” but that which all signs ofthis notation, which deny p, have in common. Hence the commonrule according to which “�p,” “��p,” “�p v �p,” “�p & �p,” etc.etc. (to infinity) are constructed” (TLP 5.512).But this then suggests that to understand denial we must also un-

derstand all the other logical constants,6 and in every context in whichthey could occur. Thus Wittgenstein remarks on how the proposition“reaches through the whole of logical space” (TLP 3.42; emphasismine). Thus, too, he regards the possibility of the Sheffer stroke(which by itself constitutes a truth-functionally complete set) as ofgreat significance, and makes use of it in his characterization of thegeneral form of the proposition: it serves as a way of expressing justthe essential interconnectiveness of all our means of representing theworld.Wittgenstein’s basic thought here would thus seem to be that, given

any picture, any means of depiction, everything we can say about theworld is in some sense laid out in advance – we know at once all thepossibilities of the existence and nonexistence of atomic facts that itcould represent. The logical constants, as the means of specifying var-ious subsets within that set of possibilities presented by the picture,then enable us to assert some particular state of affairs as the case.They allow us, that is, to make a claim that can be judged true or falseand hence will be involved in any proposition we make about theworld.It is, I suggest, just because the capacity to say something true or

false could be seen in this way to depend on a prior set of unassertedpossibilities that Wittgenstein in the Notebooks connects his conceptionwith (what he understands as) Frege’s idea of the “assumption”:

Although all logical constants must already occur in the simple proposi-tion, its own peculiar proto-picture (Urbild) must surely also occur in itwhole and undivided. Then is the picture perhaps not the simple prop-osition, but rather its prototype (Urbild) which must occur in it? Then,this prototype is not actually a proposition (though it has the Gestaltof a proposition) and it might correspond to Frege’s “assumption”


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(Annahme). In that case the proposition would consist of proto-pictures,which were projected on to the world. (NB 29–30)

Wittgenstein is here presumably referring to Frege’s claim that a judg-ment involves a movement from a “mere combination of ideas” (BEG11) – an unaffirmed thought marked in the Begriffsschrift by a horizon-tal stroke – to a statement that is asserted as true (which in theBegriffsschrift will then be prefaced by “|�,” the so-called judgmentstroke). Commentators have long been puzzled about Wittgenstein’sinterest in (and interpretation of) this Fregean idea, which he refers tonot only in the Notebooks but also at 4.063 of the Tractatus.7 But withthe above discussion, the connection to Wittgenstein’s own concernsshould now start to become clear. What the Notebooks passage calls the“proto-picture” would seem to be equivalent to the existent and non-existent atomic facts that the picture presents, or, rather, what iscommon to those facts. Since it is only with the determinate methodof projection provided by the logical constants that the picture canrepresent a particular state of affairs – that is, assert something as thecase – we might well regard the proto-picture as akin to the Fregean“assumption.”8

Of course, this is by no means to suggest that Wittgenstein’s think-ing here should simply be assimilated to Frege’s. Rather, Wittgenstein,in his characteristic way of responding to his predecessors, must beunderstood essentially as coopting the Fregean insight, taking what hesees as important in Frege’s approach and using it toward a very un-Fregean end. What is important in the notion of the assumption forWittgenstein is that it brings out how the possibility of saying some-thing determinate about the world depends logically on a prior innerconnection between language and reality, a form that is common toboth. At the same time, a clear understanding of this idea makesevident that we have no hold on that form apart from our capacity tomake true and false statements about the world.Just this idea would seem ultimately to lie behind remarks 4.063

and 4.064, which I think it is useful to quote in full:

An illustration (Bild; “picture”) to explain the concept of truth. A blackspot on white paper; the form of the spot can be described by saying ofeach point of the plane whether it is white or black. To the fact that apoint is black corresponds a positive fact; to the fact that a point is white(not black), a negative fact. If I indicate a point of the plane (a truth-


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value in Frege’s terminology), this corresponds to the assumption (An-nahme) proposed for judgment, etc. etc.But to be able to say that a point is black or white, I must first know

under what conditions a point is called white or black; in order to beable to say “p” is true (or false) I must have determined under whatconditions I call “p” true, and thereby I determine the sense of theproposition.The point at which the simile breaks down is this: we can indicate a

point on the paper, without knowing what white and black are; but toa proposition without a sense corresponds nothing at all, for it signifiesno thing (truth-value) whose properties are called “false” or “true”; theverb of the proposition is not “is true” or “is false” – as Frege thought –but that which “is true” must already contain the verb. (TLP 4.063)Every proposition must already have a sense; assertion cannot give it asense, for what it asserts is the sense itself. And the same holds of denial,etc. (TLP 4.064)

Now Wittgenstein’s conception of truth will be discussed in moredetail shortly. But it would be easy to conclude from these passagesthat he is primarily concerned to advance an extreme form of verifi-cationism, that his contention is that for a proposition to have a sensewe must first lay down some sort of rule specifying the conditionsunder which it is to count as true. Such an idea, however, runsfundamentally counter to what we have described as Wittgenstein’sconception of the self-sufficiency of sense, the notion that, as he putsit at 5.473, “logic must take care of itself.”9 Instead, we must view thispassage in connection with his earlier discussion of the picture.The claim at 2.17, we recall, is that the Form der Abbildung, the

pictorial form, is identical in the picture and what it depicts: becausethe pictorial elements have the same possibilities of combination asthe objects for which they go proxy the picture will always be a pictureof the world. It is then against the background of this common picto-rial space that the picture can be projected so as to specify a determi-nate state of affairs. In the terms of the above passage, this idea couldbe expressed by saying that it is only given the possibility of identifyinga location on the piece of paper (the analogue to the Fregean An-nahme) that I can assert that a given point is black or not black. Then,just as the possibility of representing a state of affairs requires a partic-ular way of projecting the picture, Wittgenstein here points out thatthe possibility of making a determinate assertion in the case at hand


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demands our knowing what it means for a point to be black or white.This, however, is not analogous to some special stipulation that mustaccompany the proposition but, rather, describes what it means tohave a proposition in the first place: the proposition is the setting forthof a possibility of a state of affairs, the identifying (with the help of thelogical constants) of a particular region in logical space.10 That is whyWittgenstein emphasizes that, unlike in the analogy of the spot on thepaper, there is nothing that corresponds to the assumption in the caseof the proposition without a sense – we do not first point to a regionin logical space and then decide whether it or its negation is to beasserted. Instead, to have a proposition is just to have provided our-selves with the means of arriving at what could be the case, of specify-ing a sense. What Wittgenstein sees Frege as (appropriately) reachingfor with his talk of the “entertaining” of a thought is then the ideathat the logical constants cannot accomplish this end on their own,that they must be conceived as in some sense operations on a pregivencontent. Frege’s confusion, however, is to suppose that this “pregivencontent” is itself a kind of determination of reality, rather than onlythe condition of such a possibility. Thus, Wittgenstein says that thegenuine proposition already has a sense – no further move is requiredfor it to represent a determinate state of affairs.Through this discussion we then begin to see the thinness of the

notion of a “logical constant.” For to hold that the proposition alreadyhas a sense, or that the whole of logical space is given along with thepicture (and what it presents) is to suggest that the logical constantsdo not introduce anything new into our understanding of the world.Once we have the picture with its intrinsic connection to the world, itwould seem that everything that is of significance for logic is alreadygiven: logic comprehends only how reality becomes determined. HenceWittgenstein’s oft-quoted remark: “My fundamental thought is thatthe “logical constants” do not represent (vertreten). That the logic of thefacts cannot be represented” (TLP 4.0312). Now Ogden’s rendering ofvertreten here as “represent” is somewhat misleading, particularly givenmy own translation of darstellen by this word. I suggest that “deputizefor” or “stand for” would be a better, if more awkward, translation,since (as we have seen) the term vertreten is also used at 2.131 tocharacterize the relation between the pictorial elements and the ob-jects with which they are correlated. It then becomes apparent thatWittgenstein’s point is that the logical constants cannot be construed


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as names, as additional elements of the proposition to which theremust correspond anything in the world. We correlate elements of theproposition with objects and, given the pictorial nature of the propo-sition, are then at once able to represent the full range of possible facts– no logical coordination is necessary.For Wittgenstein, then, the true import of Frege’s distinction be-

tween assumption and assertion is just the dismantling of the mostfundamental Fregean idea – the idea that “logic” constitutes a genuinesubject matter. We are meant to see that, contrary to Frege’s conten-tion, the logical functions cannot be construed along the lines of gen-uine (material) functions, that it makes no sense to suppose a domainof entities which form the special province of the logician. Nor is thisa point directed merely at Frege. Russell is even more explicitly com-mitted to the assumption of a definite logical subject matter, as isevident in his previously referred to claim that “the chief part ofphilosophical logic” is “the endeavor to see clearly the entities” thatmathematics regards as indefinable (Principles xv). He in fact goes sofar as to compare the attempt to grasp the fundamental concepts oflogic with the search for Neptune, “with the difference that the finalstage – the search with a mental telescope for the entity which hasbeen inferred – is often the most difficult part of the undertaking”(Principles xv). Russell’s approach, too, is called into question with theTractatus’ attempt to deflate the reality of the logical constants.Still, one may wonder why this claim of Wittgenstein’s should con-

stitute his “fundamental thought.” Surely there is more at issue in theTractatus than whether or not “and,” “or,” “not,” and so on stand foranything. Indeed, there is surely much more going on in Frege andRussell than the bare assertion of the existence of such entities. Perhapsthe undermining of this assumption does call into question the “Pla-tonism” inherent in the Fregean and Russellian approaches – but thatalone would hardly serve to cast aspersion on the sum total of theircontributions. Why, then, is the “nonrepresentativeness” of the logicalconstants held to be such a central point?Part of the answer, at least, has to do with the sort of move that

Wittgenstein is here making. For in holding that nothing correspondsto the logical constants, he really must be understood as attemptingto show, in a manner analogous to his treatment of the elementarypropositions, the misguidedness of the philosopher’s demand moregenerally. Just as the Bedeutungen of the names were seen to be


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absorbed into the way the propositional constituent functions in thepropositions in which it can appear, so the logical constants are incor-porated into the means by which the propositional sign as a whole iscompared with reality. Wittgenstein is then suggesting that the at-tempt to “look for” a logical entity of the Fregean/Russellian variety isnot a mere vain endeavor – as if he were claiming, to use Russell’sanalogy, that the location in space in which we hoped to find a planetis in fact empty – but a chimera: it is nonsense to suppose that an “it”could ever satisfy our search. And that makes it evident that theultimate point here is much the same as the one that emerged in thediscussion of the analysis of the elementary proposition. The moveagainst the logical constants can thus be said to be paradigmatic of theTractatus’ way of dissolving the questions of philosophy (in particular,the sorts of questions that Wittgenstein takes Frege and Russell to beconcerned with) and in this sense to be its “fundamental” thought.Indeed, the Tractatus’ Grundgedanke is explicitly anticipated in the

remarks that close the 3s:

The proposition determines a place in logical space: the existence of thislogical place is guaranteed by the existence of the constituent partsalone, by the existence of the significant proposition. (TLP 3.4)The propositional sign and the logical coordinates: that is the logicalplace. (TLP 3.41)The geometrical and the logical place agree in that each is a possibilityof an existence. (TLP 3.411)

The “logical place,” it would appear, is nothing but some state of affairs(a possible fact) that the proposition can represent; it is one positionwithin the overall coordinate system that Wittgenstein calls logicalspace. In asserting that such a place is “guaranteed” by the existenceof the significant proposition, Wittgenstein must then be seen as againemphasizing the internal nature of the relation between a propositionand what it represents: the proposition is nothing but the stipulatingof a location within a larger framework and hence cannot but pick outa logical place. The logical constants or “logical coordinates,” as theparticular ways that the propositional sign is projected on to the world,constitute part of the means by which that stipulation becomes possi-ble. But that is to say that the logical constants, instead of constitutingsome features of reality that might themselves be described, simply


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form part of the logical coordinate system within which genuine de-scriptions are made.The idea of the coordinate system is thus again central in Wittgen-

stein’s attempt to show the emptiness of the philosophical enterprise.Still, while this image brings out rather strikingly how the logicalconstants cannot be blithely included in amongst the other elementsof the world, it may appear to do so at the price of assuming a veryinflated conception of “logical space.” For does not the notion that thewhole of logical space is somehow “given in its entirety” with thepossibility of a proposition express nearly everything that philosophershave traditionally meant when they have held logic to be a priori? HasWittgenstein then not simply transposed the question of the nature ofthe supposed logical entities to one about the nature of this mysteriousa priori coordinate system – logical space?In fact, Wittgenstein’s full answer to this question is bound up with

his understanding of the logical constants as operations and hencemust await our discussion of the specification of the general form ofthe proposition. But the general direction of his response should al-ready become apparent when we recall what it really means for himto say that the picture presents the existence and nonexistence ofatomic facts. For this is simply a way of pointing out that it is the samepicture that allows us to say A and also �A, A & B as well as �A v B,and so on: the whole account of the picture, we must remember,assumes from the start the notion of the picture in use. The “field” ofwhat a picture presents – logical space itself – then grows out of, isparasitic on, what that picture can represent, by means of the logicalconstants. Thus Wittgenstein, one sentence after declaring that the“whole logical space must already be given” by the proposition, adds:“The logical scaffolding round the picture determines the logical space”(TLP 3.42; emphasis mine). The case, in other words, is in manyrespects the same as with physical space: just as we saw that the formof physical space does not constitute an a priori constraint on ourability to represent the world but, rather, emerges out of the signifi-cant use of the spatial picture, so too with logical space and the logicalpicture. Logical space, we might say, is the necessary by-product of ourability to represent the world.This is not to deny that, in a certain sense, the contours of logical

space can be described in advance. The existence of logical inference,


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as the Tractatus understands it, depends on such a possibility. Indeed,the same possibility allows Wittgenstein himself to offer his own gen-eral characterization of the proposition.11 But, as we shall see, thecentral purpose of that characterization is to make clear how we none-theless cannot understand the dimensions of logical space entirelyapart from the use, the projection of the proposition. Wittgenstein’saim is thus not to deny altogether the traditional idea of logic as apriori, but to attain greater clarity with regard to that notion. And that,for him, will mean precisely showing how little the a priori comes to:it comprehends no more than our characteristic methods of projectingthe pictorial fact on to reality.

III

Here, though, Tractarian readers of a certain mindset may well balk.For I seem to be suggesting that talk of “projection” constitutes, as itwere, the end of the story for Wittgenstein – as if seeing how thelogical dimensions of the proposition are incorporated into the pro-jecting of our pictures were akin to those dimensions’ vanishing fromthe radar screen of philosophical consideration. But doesn’t the Trac-tatus in fact hold that the possibility of projection itself requires expla-nation? And is the notion of “thinking” not introduced to fulfill justthis function?12 After all, Wittgenstein follows the above quoted seriesof claims with a remark about the “applied, thought (gedachte;“thought-through”), propositional sign” (TLP 3.5) and, at 3.11, explic-itly equates thinking with a kind of projection. It might well seem thatWittgenstein, in a manner reminiscent of Frege, is fundamentallycommitted to the assumption of a kind of mental intermediary be-tween language and the world – that it is indeed against precisely thispicture that much of the anti-mentalism of the Investigations is di-rected.13

To attribute this conception to the Tractatus would give its moveagainst the assumption of genuine logical constants a quite differentcharacter than what I have been suggesting. We must then examinemore closely Wittgenstein’s way of connecting the notions of proposi-tion, thought, and projection.

In the proposition (Satz) the thought is expressed perceptibly throughthe senses. (TLP 3.1)


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We use the sensibly perceptible sign (sound or written sign, etc.) of theproposition as a projection of the possible state of affairs. The method ofprojection is the thinking of the sense of the proposition. (TLP 3.11)The sign through which we express the thought I call the propositionalsign. And the proposition is the propositional sign in its projective rela-tion to the world. (TLP 3.12)The thought is the significant proposition. (der sinnvolle Satz; TLP 4)

The thought – the logical picture of the world – is in these passagespresented as intimately connected to the proposition; it is, we mightsay, just by means of the proposition that the thought is expressed,made manifest. The proposition, in turn, cannot be understood apartfrom the propositional sign in its significant use. Thus, rather thanhaving two entities – the thought and the propositional sign – andthen worrying over how they are to be connected, for Wittgensteinthe thought would seem to emerge precisely in and through the pro-jection of the propositional sign on to reality.The contrast of this approach with Frege’s is at once apparent. For

Frege (post-1892), the proposition (Satz), like the name, has both asense (Sinn) and a reference (Bedeutung). The proposition’s Bedeutungis a truth value, its Sinn, a thought. While the relation between apropositional sign and a thought is on this account somewhat obscure– the latter presumably cannot be named by the propositional sign,since then it would constitute its Bedeutung – Frege over and overinsists on the independent, genuine existence of the Gedanke.14 Forhim, this assumption is unavoidable if the objectivity of language –which is to say the possibility of science, of communication in general– is to be secured.Far from adopting a Fregean model of the relation of thought and

propositional sign, it begins to seem as if the Tractatus is essentiallyconcerned to advance a diametrically opposed conception. In intro-ducing the notion of the projected propositional sign, Wittgensteinwould appear to be suggesting that it is simply unnecessary to assumethe existence of a separate thought, a vaporous “proposition,” hover-ing over the propositional sign. His ultimate aim, we might then sup-pose, is just to restrict Frege’s extravagant ontology, to propose acounter theory in which the thought is “immanent” in the proposi-tional sign.But to put the matter this way is now to overstate Wittgenstein’s

difference with Frege – or, rather, to misdescribe the real character of


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that difference. For one thing, it appears to leave Wittgenstein open tothe charge of subjectivism (one thinks here of Frege’s objectionsagainst formalism): to simply deny the existence of the Fregean Ge-danke would seemingly be to reject the objectivity it is supposed toguarantee. The embrace of subjectivism, however, is not only veryforeign to the Tractatus in general but also specifically ignores theextent to which Wittgenstein seeks to accommodate a notion of objec-tivity within his conceptions of thought and thinking:

We cannot think anything unlogical, for otherwise we should have tothink unlogically. (TLP 3.03)It used to be said that God could create everything, except what wascontrary to the laws of logic. The truth is, we could not say of an“unlogical” world how it would look. (TLP 3.031)That logic is a priori consists in the fact that we cannot think illogically.(TLP 5.4731)

Indeed, these passages have a distinctly Fregean ring to them, inparticular hearkening back to the Grundgesetze discussion of our sup-posed inability to understand beings “whose laws of thought flatlycontradicted ours” (BLA 14).15 Wittgenstein’s relation to Frege on theissue of the nature of thinking evidently cannot be construed in termsof flatly opposed positions.One solution to these interpretational difficulties would be to see

the Tractatus as retaining the Fregean notion of thought, but, in effect,purging it of any connection with ontology. That is, Wittgenstein is tobe understood as seeking to account for what one might think of asthe objective dimension of language – in effect, the possibility of suc-cessful communication – but to express that only in logical, ratherthan ontological terms. In this sense he could be said to be getting atthe heart of Frege’s view, since one might well argue that, for thelatter, the real criterion of identity for thoughts ultimately is given bya sentence’s role in logical inference patterns.Now such an interpretation is, I would suggest, correct as far as it

goes. But even here we must caution against a too facile incorporationof Wittgenstein’s views within a Fregean framework. For while theTractatus retains Fregean language regarding the normative status oflogical laws, its central aim is always to shift our understanding ofwhat that normativity comes to. The nature of this shift is alreadyapparent in the remark following 3.031, the remark about the impos-


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sibility of illogical thought quoted above: “To represent (darstellen) inlanguage anything which ‘contradicts logic’ is as impossible as in ge-ometry to represent by its co-ordinates a figure which contradicts thelaws of space; or to give the co-ordinates of a point which does notexist” (TLP 3.032). Why can’t we give the coordinates of a point whichdoes not exist? The answer, of course, is that to specify coordinates ona graph is to specify a point. This is not to attribute some magicalcreative properties to such a specification, but is simply a way ofbringing out that we do not have a notion of a point apart from theway it is, or rather could be, identified. The same will then be said tohold with regard to “thinking” and “region within logical space.” Wemight assert that to think is always to specify a region in logical space,but that is just because the projecting of the pictorial fact on to reality– its being thought – structures this space, the logical coordinate system:thinking and logic, we could say, are given together.Wittgenstein thus attempts to preserve the Fregean insight about

the impossibility of illogical thought – even, as I suggested above, toget at the heart of what he takes to be Frege’s concern. Once more,though, it becomes apparent how, for the Tractatus, the exposing ofthe heart of a philosophical question is equivalent to its disappearance;the necessity that is said to belong to thought’s respecting of logicalboundaries comes at the price of the utter emptiness of this claim. Wemight then express Wittgenstein’s general stance toward the notionsof thought and thinking in this way. Clearly, he is not concerned todispute the assertion that there is thinking, that the propositional signis not capable of interpreting itself. Of course we think. The realquestion concerns the significance of this truism, the suitability of thenotions of thinking and thought for use as central tools of philosophi-cal analysis. What Wittgenstein aims to bring out is how the significantproposition with which we begin any analysis is already “thought,”how we start out with “the propositional sign in its projective relationto the world.” This idea, as we have seen, informs every aspect of hisdiscussion of the picture: the picture’s capacity to represent some par-ticular state of affairs presupposes the projecting both of the pictorialelements (the possibilities of which constitute the picture’s Form derAbbildung), and the pictorial fact (the possibilities of which constitutelogical space) on to reality. Thinking permeates the picture – and sothe possibilities for one of these notions cannot but coincide with thepossibilities for the other. But that at the same time expresses the


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weakness of our hold on the notion of thinking; it brings out how“thought” is no closer to us, so to speak, than the logic it would clarify.Far from postulating a mental bridge connecting the picture to reality,as Hacker suggests,16 Wittgenstein suggests that it is the mental realmitself that needs to be accessed – and the way is via the picture.

IV

Still, if “thinking” will not play an explanatorily privileged role in theTractatus’ discussion of logical space, we must come to understandhow, for Wittgenstein, we can characterize this latter notion and whatsuch a characterization comes to. We shall address this issue througha consideration first of the Tractatus’ notion of tautology and then ofits specification of the general form of the proposition.Both of these notions may be approached through further reflection

on the Tractarian conception of “sense” and its relation to “truth.”These central terms are introduced at the close of Wittgenstein’s initialdiscussion of the picture. First, then, 2.221: “What the picture repre-sents is its sense (Sinn).” Since, as we have seen, the picture is alsosaid to “represent” some particular state of affairs in logical space, thissuggests that such an assemblage of facts is to be regarded as the senseof that picture. 4.031 confirms the point: “One can say, instead of,This proposition has such and such a sense, This proposition represents(darstellt) such and such state of affairs (Sachlage).” Which state ofaffairs is then to be identified with the picture/proposition’s sense? Itmay appear as if Wittgenstein gives conflicting responses to this ques-tion. For at 4.063, he suggests that the sense is given through knowingwhat obtains when the proposition is true: “In order to be able to say‘p’ is true (or false) I must have determined under what conditions Icall ‘p’ true, and thereby I determine the sense of the proposition.”17

It appears from 4.2, however, that I only know a proposition’s sensewhen I know what it means to be true and false: “The sense of aproposition is its agreement and disagreement with the possibilities ofthe existence and nonexistence of the atomic facts”; sense here in-cludes all of a proposition’s truth-possibilities. This appearance of con-flict disappears, however, when we recall from our earlier discussion18

that the Sachlage represented by the proposition is itself conceived ascontaining both an existent and nonexistent atomic fact – that is, apositive and negative fact. The Sachlage, in other words, is what Witt-


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genstein at 4.063 likens to a solid substance and the space within it,in which a body may be placed. To represent a sense is then tohighlight, as it were, one of the twin aspects presented by the picture.19

But that highlighting always takes place against the backdrop of itscomplement – which is to say that an understanding of the proposi-tion’s truth conditions carries with it an understanding of its falsifica-tion conditions and vice versa. As Wittgenstein remarks at 3.144, thesense of a proposition is like an arrow, orienting us in this way towardthe facts with which it is associated.Now taken in isolation, these claims may seem to commit Wittgen-

stein to a kind of realism of facts reminiscent of Russell’s logical at-omism.20 After all, one might ask, is he not suggesting that a priorcognizance of a fact (or set of facts) is necessary to understand thepicture’s sense – and, therefore, that facts, possible as well as actual,must be assumed to be brutely “out there”? And are not these factsregarded as responsible for “making” the picture (or proposition) trueor false?21 Given what we have said about the first part of the picturetheory alone, however, it should be clear that Wittgenstein cannotintend to maintain any such position. The pictorial elements and theirreal world counterparts are held to have the same possibilities ofcombination: the force of this assertion, we have seen, is to bring outthe inseparability of the connection between the picture and reality,to suggest that the fact is only given, only structured or shaped,through the picture that depicts it. Wittgenstein, rather than endorsinga full-blown Russellian ontology of facts – positive, negative, particu-lar, general, and so forth – is thus from the start seeking to bring outthe emptiness of this whole conception. (We must not forget, after all,that 4.1272 declares any talk of facts to be nonsense.) In identifying apicture/proposition’s sense with a state of affairs, he should then beseen really as stressing the flip side of what 4.014 refers to as the“pictorial internal relation which holds between language and theworld.” That is, just as earlier he emphasizes how we can have nohold on “fact” apart from the particular means we use to represent theworld, at this point he is stressing how our understanding of thenature of that means of representation is likewise inseparable fromthe facts toward which it is directed.This, of course, is not to suggest that there is no way in which the

world and the picture can be compared. On the contrary, it is justbecause some kind of comparison can be effected that we are able


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to speak of truth or falsity at all. Nonetheless, we must recognize howwe come to this point only after every move having to do with thelogic of depiction has been taken. 2.173 helps to clarify this point: “Apicture represents its subject from a position outside it. (Its standpointis its representational form [Form der Darstellung]). That is why a pic-ture represents its subject correctly or incorrectly.” The Form der Dar-stellung comprises the various ways of projecting the picture on toreality (the various ways, that is to say, that a picture can represent);the picture can be said to stand “outside” its subject matter becausethe method of projection always operates on a completed picture, as itwere, on the pictorial elements taken against the background of theForm der Abbildung.22 Given that this form is common to the pictureand what it depicts, the whole space of facts presented by the picturewill necessarily belong to the world. Once the picture is then projectedin a determinate manner, it will represent exactly one state of affairsas obtaining, fixing what we are to expect to the extent that, asWittgenstein later puts it, “one only needs to say ‘Yes’ or ‘No’ to [thepicture] to make it agree with reality” (TLP 4.023). The “yes” or “no,”of course, corresponds to the picture’s truth or falsity. But since whatthe world will look like in either case has been completely describedbeforehand, this verdict is, so to speak, an easy call – it is simply amatter of looking.To refer to the Tractatus’ remarks about truth as constituting a “cor-

respondence theory,” as is typically done,23 is then not wrong, but itpotentially misses the point. For this phrase might tend to suggestsome sort of agreement between two distinct sets of facts, while Witt-genstein’s primary aim, as I have indicated, is to show just the intrinsicconnection between the picture’s content and the world: it is preciselybecause a possible state of affairs is, as he puts at 2.203, “contained”in the picture that any sort of agreement between the two can berealized. The claim about the need to compare the picture and reality,rather than constituting part of an elaborate correspondence theory,is thus really meant to drive a wedge between the notion of truth andany concern with sense and the conditions of representation (theproper concerns of the philosopher). Wittgenstein’s purpose, in otherwords, is to get us to see that the role of the picture is only to prepareus to meet reality, to enable us to say how things might stand – thathow things are in fact is not something that can be gathered from thepicture alone. It may be helpful to reflect here on Wittgenstein’s alter-


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nate metaphor of the ruler. To postulate an a priori true picture wouldbe like postulating a measurement that is correct simply in virtue ofits constituting a position on the measuring scale. But that is nonsense:we have genuinely taken a measurement – we can speak of “correct”and “incorrect” measurements – only when the ruler has been laidagainst some object in the world, if only from afar. In the same way,the picture requires its corresponding reality, the possibility of its beingcompared to something outside itself, if it is to have the chance ofbeing judged as true.Wittgenstein makes this idea explicit at the close of his initial dis-

cussion of the picture: “It cannot be discovered from the picture alonewhether it is true or false. There is no picture which is a priori true”(TLP 2.224–5). A picture that does not require comparison with realitywill eo ipso not represent a possible state of affairs in the world – thatis, will not have a sense – and hence will not be a genuine picture.Now for the Tractatus the primary, indeed sole, examples of such apriori true pseudo-pictures are, of course, the “statements” of formallogic. Implicit in the picture theory, then, is Wittgenstein’s later dispar-agement of the sentences of logic – the “tautologies” and “contradic-tions” – as “senseless” (sinnlos; see TLP 4.461, 4.4611, 5.132).4.462 makes quite evident how this central idea of the Tractatus is

connected with the earlier remarks about the picture:

Tautology and contradiction are not pictures of the reality. They repre-sent (darstellen) no possible state of affairs. For the one allows everypossible state of affairs, the other none. In the tautology the conditionsof agreement with the world – the representing relations (die darstellen-den Beziehung) – cancel one another, so that it stands in no representingrelation to reality.

The “representing relations,” as the various ways in which the picturecan be compared with reality, are equivalent to what we have earlierreferred to as the methods of projection of the pictorial fact. Wittgen-stein is suggesting that, while some method of projection is necessaryif a proposition is to represent a particular state of affairs in logicalspace, in certain instances these methods come in conflict. Suppose,for example, we construct a string of signs of the form p v�p: it is asif, to build on Wittgenstein’s metaphor at 4.463, the space that iscarved out by p is immediately filled in with the “solid substance” thatbounds it; the resulting proposition thus leaves reality absolutely


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untouched. (Although we might be pleased with such a result froman environmental perspective, from the standpoint of communicationit is less than optimal.) Hence “p v �p” will not say anything, is atautology and not a genuine proposition, even while it relies on thesame rules that enable, for example, “p v �q” to represent. The verything that allows propositions to express a definite sense can alsoserve, it would seem, to deprive them of that sense. For this reasonWittgenstein denies that logical propositions can be completely ex-cluded from a language: “Tautology and contradiction are, however,not nonsensical (unsinning); they are part of the symbolism, in thesame way that “0” is part of the symbolism of Arithmetic” (TLP4.4611). For this reason too (or, at least, in part for this reason) hespeaks of language as “disguis[ing] thought” (TLP 4.002) and praisesRussell for “hav[ing] shown that the apparent logical form of theproposition need not be its real form” (TLP 4.0031): just because “p v�p” and “p v �q” have superficially the same form (rely on the samemethod of projection), we should not at once assume that these arepropositions of the same sort. Sense and senselessness spring from thesame root and so care must be taken – thoughtfulness exercised – totease them apart.This idea of what we might call the delicacy of sense is quite central

and needs to be elaborated on. First, it should be noted that the basicpoint applies not only to the propositions of logic but also to thenonsensical claims of philosophy, albeit in a somewhat different way.To be sure, Unsinnigkeit is said in the Tractatus to arise not from conflictbetween the picture’s “representing relations,” but from a failure toconstruct a picture in the first place; in such cases, Wittgenstein says,“we have given no meaning (Bedeutung) to some of [the proposition’s]constituent parts” (TLP 5.4733).24 Nonetheless, like the propositions oflogic, most of these pseudo-propositions – and certainly all those thatWittgenstein is chiefly concerned to expose (e.g., “1 is a number,” or“There are objects”) – have the appearance of ordinary sentences.Indeed, as I pointed out in the Introduction,25 they would not other-wise have the capacity to mislead. The discernment of what Wittgen-stein calls “nonsense” then requires a sensitivity to the multiplicity oflogical forms, the good judgment to be able to recognize when theinner syntax of the proposition has been violated. We could say thatthe central purpose of the discussion of analysis in the 3s is in fact tomake precisely this point: to hold that the forms of the elementary


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propositions are not give a priori is just to suggest that sense is notgiven simply by virtue of a sentence’s assuming a particular appear-ance.26 The Tractatus does not and could not attempt to provide us withan external mark of significance.Of course, all of this is simply a different way of putting what has

been my fundamental contention throughout – namely, that the Trac-tatus’ method is essentially dialectical, that its aim is always to under-mine the central questions of philosophy from the inside, withoutmaking appeal to any kind of fixed criteria of sense and nonsense.Still, the difficulties and peculiarities of this whole approach are partic-ularly evident when we focus on the analysis of the propositions oflogic. For it would seem that the assertion of the tautological natureof such propositions – the fact that they say nothing about the world –is central to the Tractarian response to the Principia and Begriffsschrift;Wittgenstein appears to rely on this point as having been firmly estab-lished. But we must ask ourselves: How has this been accomplished?It is one thing to grant that a form of words cannot be recognized as aproposition of logic simply from its superficial appearance, but quiteanother to suppose that, once such a proposition has somehow beenidentified, one must regard it as sinnlos, as representing no state ofaffairs. Has Wittgenstein actually shown that the propositions of logichave this property? At 4.466, he asserts: “In other words, propositionsthat are true for every state of affairs cannot be combinations of signsat all, since, if they were, only determinate (bestimmte; perhaps “partic-ular” would be better here) combinations of objects could correspondto them.” But why does the fact that “p v �p” pictures no particular ordeterminate state of affairs necessarily prevent this expression fromcomposing a legitimate combination of signs?27 Could we not equallysay that such symbols just constitute very general pictures? One mightsuppose that Wittgenstein would buttress his argument with the claimin 6.113: “It is the characteristic mark of logical propositions that onecan perceive in the symbol alone that they are true; and this factcontains in itself the whole philosophy of logic.” But if this claim restson the possibility of a general decision procedure for the whole of logic– if, that is, all logical propositions fail to be pictures of the world forthe reason that we are imagined to have an a priori test for their truthand falsity28 – then this part of Wittgenstein’s argument seems to fallto the ground. For we cannot have a general decision procedure evenfor all of first order logic, as was shown by Church and Turing in 1936.


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The question, then, would appear to stand: How has Wittgensteinproven that logical propositions are senseless tautologies?The answer, of course, is that he has not proven this, any more

than he has proven that the world (really) is all that is the case; as Ihave maintained throughout, “proof” has no place in the philosophicalspace in which the Tractatus moves. But to grasp fully what this gen-eral point comes to in this case, we need to consider the more ex-tended discussion of tautology in the 6.1s. Toward the beginning ofthat discussion Wittgenstein states:

Theories which make a proposition of logic appear substantial are al-ways false. One could e.g. believe that the words “true” and “false”signify two properties among other properties, and then it would appearas a remarkable fact that every proposition possesses one of these prop-erties. This now by no means appears self-evident, no more so than theproposition “All roses are either yellow or red” would sound even if itwere true. Indeed our proposition now gets quite the character of aproposition of natural science and this is a certain symptom of its beingfalsely understood. (TLP 6.111)

Here Wittgenstein is, in essence, laying down conditions of materialadequacy for an analysis of the logical proposition: any acceptableanalysis must make evident how such propositions are not true andfalse like the “substantial” propositions of natural science. Indeed, thatanalysis also must reveal how the strings of logic are not genuinepropositions in the first place since, as he implies in this passage (andhas earlier made clear in the discussion of the picture), the possibilityof truth and falsity and propositionhood are given together, are inter-nally related. What is important about this passage, then, is that itmakes evident that Wittgenstein makes no pretense of being drivenby certain previously unrecognized facts, by some overpowering ar-gument, to declare the special nature of the logical proposition.Rather, he starts off with the belief that this sort of proposition cannotbe approached as if it were on par with a claim of natural science andthen attempts to find various means to make this distinction compel-ling, to persuade us to look at “p v �p” from other than this “false”(“misleading” would perhaps be a better word here) perspective. Therecognition of something peculiar about the status of logical proposi-tions is, in other words, integral to the whole perspective the Tractatus


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seeks to articulate. But that would already seem to indicate that theTractarian claim about those propositions’ tautological nature cannotbe viewed simply as a self-standing assertion that awaits its properjustification.It is in this context, then, that Wittgenstein makes the above-quoted

remark (TLP 6.113) about the “truth” of the logical proposition beingperceivable in the symbol alone. Now because of this claim, as well asclaims like 6.126 (“Whether a proposition belongs to logic can becalculated by calculating the logical properties of the symbol.”), a num-ber of commentators have assumed that the Tractatus’ whole positionrests on the assumption of a general decision procedure, a point wealluded to above. Of course, Wittgenstein explicitly acknowledges thathis “intuitive method” of exposing tautologies – a method that isessentially equivalent to the use of truth tables – is applicable “in casesin which no sign of generality occurs in the tautology” (TLP 6.1203);he certainly does not seem to imagine himself as having provided atechnique that is applicable to the whole of logic.29 Regardless, though,even if he did assume that a general decision procedure were availa-ble, we must ask ourselves what consequences this mistake wouldhave. Must we conclude, like Black, that it would prove “fatal toWittgenstein’s philosophy of logic”?30

A consideration of this question will help to make clearer the Trac-tatus’ stance on this whole matter. Let us suppose, counterfactually,that we do have an effective method of determining validity for all offirst order logic. We then would stand in the same relation to thewhole of logic as we do at present to the propositional calculus. Withregard to the latter we now can ask: does our ability to show thatsome sentence comes out true on every truth-value assignment to itscomponent parts prove its tautologous nature? In a certain sense onemay answer “yes,” since it now has become customary (in large partas a result of the Tractatus) to take this as a definition of “tautology.”31

But, of course, the real question here concerns the basis of this con-vention or, perhaps better, the implications of adopting it. Are we, inso doing, forced to regard tautologies as senseless, pseudo-propositions? It seems not. Indeed, it is quite common to take thetruth table method as revealing tautologies to be truths that holdin “all possible worlds.”32 Far from showing the emptiness of suchexpressions, the Tractarian technique can be used to buttress an


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understanding of them as transcendent, “super truths.” Given thepossibility of a general decision procedure, the same could then besaid of all the propositions of logic.It may appear as if I am now suggesting that Wittgenstein is unwit-

tingly attempting to prove the opposite of what he had intended aboutthe nature of the logical proposition. But that is not the conclusion tobe drawn here. Instead, the point is to see the independence of thequestion of the existence of a general decision procedure from thephilosophical moral of the Tractatus’ remarks; it is to start to bring outhow uncomfortably the notion of proof fits in this context. This, Isuggest, is precisely the force of the close of 6.126:

We prove a logical proposition by creating it out of other logical propo-sitions by applying in succession certain operations, which again gener-ate tautologies out of the first. (And from a tautology only tautologiesfollow.)Naturally this way of showing that its propositions are tautologies isquite unessential to logic. Because the proposition, from which the proofstarts, must show without proof that they are tautologies.

Similarly we find:

Proof in logic is only a mechanical expedient to facilitate the recognitionof tautology, where it is complicated. (TLP 6.1262)All propositions of logic are of equal rank; there are not some which areessentially primitive and others deduced from these.Every tautology itself shows that it is a tautology. (TLP 6.127)

Now, these remarks are difficult and must be treated carefully. Itwould be easy to suppose that this talk of tautologies showing them-selves as such rests on the possibility of some special moment ofinsight, as if we might grasp via an act of intuition the tautologicalessence of the logical proposition. One might think that this wouldserve to explain why proof would be viewed as ultimately unnecessaryin the case of recognizing tautologies. We have seen, though, that thenotion of showing is never used in connection with any such conjec-tured psychological state. Wittgenstein in fact is explicit in his denialof the relevance of psychological states to the issues with which he isconcerned. This is evident in his dismissal of the philosophical signifi-cance of psychology – “Psychology is no nearer related to philosophy,than is any other natural science” (TLP 4.1121) – but even more so at


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5.552: “The ‘experience’ which we need to understand logic is notthat such and such is the case, but that something is; but that is noexperience.” Invoking magical flashes of insight will be of no use toWittgenstein (or to us) in clarifying how logical propositions can besaid to show their tautologous nature.I suggest instead that we view these remarks as reflections on what

it means to call something a tautology. Wittgenstein says that one wayto prove a proposition of logic is by generating it from other suchpropositions by the application of certain formal rules. Such a proce-dure is followed in the “old logic,” as Wittgenstein calls it in “NotesDictated to G. E. Moore in Norway”(NB 109) – that is, the formalsystems of the Principia and Begriffsschrift (and Grundgesetze). His con-tention here, however, is not that this is an inadequate method ofproof that is to be scrapped in favor of a generalized version of thetruth table method. To be sure, the systems of Frege and Russell, withtheir reliance on axioms and rules of inference, are viewed as givingus a misleading conception of the nature of logic, as we shall discussshortly. But their method fares no worse than the Tractatus’ in termsof what it actually proves about the nature of the logical proposition:in either case, Wittgenstein is suggesting, all that is shown is that agiven proposition “belongs to logic” (TLP 6.126) – that is, that it is ofa certain form, that it can be grouped along side certain other linguisticsigns.33 While the truth table method may more clearly display theuniform character of a certain class of propositions, the real point isthat this “mechanical expedient” does not, any more than an axio-matic method of proof, tell us what that character comes to; once morewe see that it makes no sense to speak of proof in connection withthe ascription of the term “tautology” to a proposition. Indeed, itwould seem that we misunderstand the Tractatus’ use of this term ifwe imagine it to refer to any sort of “property” that may or may notbe found to belong to a proposition. For Wittgenstein, a tautology isinstead part of what a particular linguistic form is. Such forms “showthemselves” to be tautologies just because having this nature is boundup with the entire role that they play, with the way they function inour language.This point can be made clearer through a consideration of the

nature of the significant sentence’s content. At 4.31 and 4.431, Witt-genstein shows how the proposition’s “truth conditions” – what wehave seen to be the sense of the proposition – can be set out in the


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now familiar form of a truth table. Thus the truth possibilities of theelementary propositions and various combinations of their resultingtruth values are listed, and the truth functional nature of the molecu-lar proposition made perspicuous. Now it is important to emphasizethat, for Wittgenstein, the truth table can itself be construed as anexpression. He remarks: “A proposition is the expression of agreementand disagreement with the truth-possibilities of the elementary prop-ositions” (TLP 4.4). And at 4.431: “The proposition is the expressionof its truth-conditions” (emphasis mine). If we standardize the order-ing of the truth-possibilities of the elementary propositions in thetruth tables, then “the last column is by itself an expression of thetruth-conditions” (TLP 4.442) and constitutes a propositional sign. Ofcourse, Wittgenstein must not be understood as thereby suggestingthat “(TTFT) (p,q)” is the preferred expression, that it somehow con-stitutes what we really mean when we assert “p � q.” On the contrary,his point here is just to bring out the deceptive nature of this demandfor the “real sense” of a sentence. “(TTFT) (p,q)” and “p � q,” he issuggesting, are equivalent expressions; the first can, for certain pur-poses or in certain contexts, simply replace the second.34 But thatmeans that the philosopher’s interest in sense – the desire for a properspecification of what that sense is – cannot find its fulfillment in eitherof these expressions as such. This desire is instead satisfied by seeingwhat is common to these symbols and all others that could replacethem; what “p” “really” says emerges just through the possibility oftranslating between equivalent means of expressing this same sense.The sense of “p” is, as Wittgenstein asserts at 4.022 and 4.461, onlyshown.In the same way that the significant proposition shows its sense,

then, the logical proposition can be said to show that it is a tautology.Wittgenstein explicitly draws the connection between these ideas at4.461: “The proposition shows what it says, the tautology and thecontradiction that they say nothing.” We must, however, be clear onthe nature of this analogy. For the point is not that being tautologousis, like the sense of a genuine proposition, that which the logicalproposition says – the latter, since it is sinnlos, does not say anything.Instead, what the Tractatus is suggesting is that we stand in the sameposition when we ask for the sense of a proposition as when we askwhy it is tautologous. Certainly, in both cases one can offer some sortof response to this question: to a confusion about p’s sense we can, as


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I have just been emphasizing, provide alternate ways of saying thesame thing; similarly, we have seen that Wittgenstein holds open thepossibility of a number of different methods of exposing tautologies(of what at 6.1263 he calls “proof[s] in logic”). But the key idea is thatall such answers would seem to stand on the same level as what isquestioned about.It is in the acknowledgment of this point that we see the incoher-

ence of asking for an ultimate justification for the ascription of “tau-tology,” for some underlying something to which we can appeal.There is, one might say, nothing hidden from us, no new facts thatneed to be brought to light. Instead, Wittgenstein’s real aim in thiswhole discussion is only to draw our attention to a difference of form:he is emphasizing how unlike the role of “p v �p” is from that of “p v�q” and, by terming the former a tautology, urging us to take thatdifference in a certain way. To grant this, however, is just to grant thatthe assertion about the tautologous nature of the proposition of logic,rather than being put forth as a self-standing claim, an attempt to offeran overarching characterization of logical truth, is as dialectical a moveas any other in the Tractatus. It takes its significance precisely from thetendency to assimilate “p v �p” and “p v �q,” the assimilation thatWittgenstein sees as lying at the heart of Frege and Russell’s concep-tion of logic as a science of maximally general truths. Shorn from theinterplay with such a tendency, from the desire for insight into theworld’s essential nature that it bespeaks, the text’s claims about tautol-ogy have no standing whatsoever.What this suggests, in turn, is that the Tractatus’ whole point in this

context is contained in the details of its account of the propositions oflogic, in its particular way of distinguishing such linguistic forms fromsignificant utterances. One means the text has of drawing this distinc-tion involves the possibility of what 6.126 calls “calculating the logicalproperties of the symbol.” If we consider this phrase by itself, it is quitenatural to suppose that Wittgenstein is here referring to somethinglike a decision procedure.35 But 6.126, like all of the remarks in the6.1s, must be read in light of the Tractatus’ discussion of the pictureand its subsequent account of analysis. Let us look at this passage nowin its entirety:

Whether a proposition belongs to logic can be calculated by calculatingthe logical properties of the symbol.


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And this we do when we prove a logical proposition. For without trou-bling ourselves about a sense and a meaning, we form the logical prop-ositions out of others by mere symbolic rules (Zeichenregeln; “rules dealingwith signs”).We prove a logical proposition by creating it out of other logical propo-sitions by applying in succession certain operations, which again gener-ate tautologies out of the first. (And from tautology only tautologiesfollow.)Naturally this way of showing that its propositions are tautologies isquite unessential to logic [emphasis mine]. Because the propositions,from which the proof starts, must show without proof that they aretautologies.

Notice, first, the structure of Wittgenstein’s claims. He does not saythat if anything is a proposition of logic, then it must be provable bylogical properties of the symbol. On the contrary, he only speaks ofwhat happens “when we prove a logical proposition.” Rather thanasserting something about what must be the case for every possibleproposition of a certain form, as he would if he were relying on theidea of a general decision procedure, he is only concerned to describewhat happens in those instances where a proof is available.Any such proof, he suggests, will involve the recognition of a fea-

ture of the symbol.36 Now, we recall that a symbol or expression forWittgenstein is any part of a proposition that contributes to its senseand that it is properly presented by a variable. We saw that the symbolcan serve as a way of showing what is common to a particular class ofpropositions and thus of characterizing the meanings of the names. Inspeaking at this juncture of a “property of the symbol,” Wittgensteinwould then seem to have moved up a level – he is concerned withwhat is common to a number of classes of propositions.37 Of course,since, as I have suggested, there is for Wittgenstein no logical hierar-chy of variables, this higher order property will be signified simply bya variable (rather than by, say, a second order variable), just like theBedeutungen of the names. Nonetheless, the possibility of recognizingsuch a property is significant. For it necessarily involves focusing onthe use of the picture as a pictorial whole or fact – the ways that it can“represent,” in the Tractarian sense of the term. We can refer to prop-erties of symbols only when we ignore everything having to do withthe inner constitution of some class of propositions (their particularlogico-pictorial forms) and consider no more than what is common to


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their capacities to be projected across logical space – that is, whatallows them to represent some particular state of affairs in the firstplace. The Tractatus’ claim is then that proof of the logical propositionrelies on this common element alone.Certainly, this point is evident when we consider a proof via the

use of a truth table: this device allows us to see clearly that the truthof, say, “p v �p” can be determined with reference only to the truthpossibilities of this propositional schema (its mode of projection). Un-like in the case of the significant proposition, we do not take intoaccount the specific content of “p,” but only how the proposition isconstructed. The point can also be seen, however, by reflecting on theaxiomatic style of proof characteristic of the Frege and Russell systems– in fact it is the latter that Wittgenstein appears to have chiefly inmind in this passage, as I implied above. For, according to Wittgen-stein, proof in the Principia is simply a matter of demonstrating thatone linguistic form can be generated out of another solely through theapplication of “rules dealing with signs.” Here, too, it would seem,truth is determined just by showing how a proposition is constructed.Given this way of construing the propositions of logic, the nature

of their connection to reality begins to become clear. At 6.12, Wittgen-stein puts it this way:

The fact that the propositions of logic are tautologies shows the formal –logical – properties of language, of the world.That its constituent part connected together in this way give a tautologycharacterizes the logic of its constituent parts.In order that propositions connected together in a definite way may givea tautology they must have definite properties of structure. That theygive a tautology when so connected shows therefore that they possessthese properties of structure.

This passage suggests that Wittgenstein’s point is not simply, as is oftensuggested, that genuine propositions state something, while the prop-ositions of logic only show formal aspects of language and reality38

(indeed, 4.121 makes clear that it is the genuine proposition thatshows logical form). Rather, he says that the fact that the propositionsof logic are tautologies is what shows those aspects. The Sinnloskeit ofthe logical proposition is then key: it is just through the disintegrationof sense that results from the attempt to combine certain strings ofsigns into propositions that particular internal features of language/


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reality come to the fore. As one might put it, to recognize a string ofsigns as a tautology is to recognize that that string is not itself attempt-ing to say something, but only serving as a way of characterizing whata number of (genuine) propositions have in common. But this is tosuggest that the propositions of logic are, for Wittgenstein, not propo-sitions at all, but, as we implied above, variables – variables that reflectproperties of the symbol. Such “propositions” can only show, sincethey ultimately constitute no more than certain means of describingan already given propositional class.The full force of these considerations is then felt with the illustra-

tion that Wittgenstein provides at 6.1201: “That e.g. the proposition“p” and “�p” in the connexion “�(p & �p)” give a tautology showsthat they contradict one another. That the proposition “p � q,” “p”and “q” connected together in the form “(p � q) & (p):�: (q)” give atautology shows that q follows from p and p � q. That “(x).fx: � :fa” isa tautology shows that fa follows from (x).fx, etc. etc.” What his ex-amples bring out is that the internal features of language and realitywith which he is here concerned, the properties of the symbol, arenothing other than what we normally think of as inferential connec-tions between propositions. To say that, for example, “(p � q) v �(p �

q)” is a tautology is simply to describe a given class of propositions, tobring out a certain feature they have in common. And that, Wittgen-stein is claiming, is all that we are doing when we say that “q” followslogically from “p” and “p � q.”This is precisely the view that is put forward in the Notebooks: “Log-

ical propositions are forms of proofs: they shew that one or more prop-ositions follow from one (or more)” (NB 109). The same point is made,albeit somewhat more obscurely, at 6.1264 of the Tractatus: “The sig-nificant proposition asserts something, and its proof shows that it isso; in logic every proposition is the form of a proof. Every propositionof logic is a modus ponens represented in signs. (And the modusponens can not be expressed by a proposition).” The proposition oflogic serves to, as it were, stamp some class of genuine propositions,to show how the members of that class share a particular form. Wethus see even more clearly why, for Wittgenstein, the tautologousnessof such propositions is regarded as basic. For this is simply to bring outthat the proposition of logic serves as itself a way of characterizing, asa paradigm in this particular “language-game.” Nothing can underliethe recognition of tautology because it is that very tautological nature


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that we rely on in describing the internal features of a given class ofpropositions.Wittgenstein connects this point with the fact that “we often feel as

though ‘logical truths’ must be ‘postulated’ by us” (TLP 6.1223). Thisfeeling reflects the recognition that the propositions of logic do notstand on their own, that they, in some sense, depend for their life onwhat we do. But Wittgenstein wants to bring out how it is nonethelessmisleading to describe matters that way: “We can in fact postulate [the‘logical truths’] in so far as we can postulate an adequate notation”(TLP 6.1223). This same idea is elaborated on at 6.124:

The logical propositions describe the scaffolding of the world, or ratherthey represent (darstellen) it. They presuppose that names have meaning(Bedeutung) and that elementary propositions have sense. And this istheir connection with the world. It is clear that it must show somethingabout the world that certain combinations of symbols – which essen-tially have a definite character – are tautologies. Herein lies the decisivepoint. We said that in the symbols which we use something is arbitrary,something not. In logic it is only the latter that expresses: but that meansthat logic is not a field in which we express what we wish with the helpof signs, but rather one in which the nature of the absolutely necessarysigns speaks for itself. If we know the logical syntax of any sign lan-guage, then we have already been given all the propositions of logic.

To say that logical propositions presuppose that names have meaningand that elementary propositions have sense is again to emphasize theprimacy of a notation. It is to get us to see how the propositions oflogic ride on the back of the genuine propositions and thus have nostatus apart from the latter. The logical proposition indeed reflectssomething about language and the world. But that is precisely becausethe values of this variable are propositions: in describing them we ipsofacto describe something about the reality with which they are con-cerned. The connection of logic with the world is preserved, one mightsay, at the price of any interest in pointing it out.Still, the Tractatus’ account of the propositions of logic as tautologies

is meant to do more than suggest that (what this text takes to be) thestandard approach to logic – the Frege/Russell formalization of logi-cal inference by means of axioms and so-called rules of inference – ismerely uninteresting or superfluous. Instead, Wittgenstein is ulti-mately concerned to claim that the very attempt to engage in thissort of formalization is an indication of a deep confusion. What he


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understands to be the real motivation for such an enterprise is implicitin the above passage: it is the desire for us to specify the “nature of theabsolutely necessary signs,” rather than allowing the signs to “speakfor themselves.” How are we to understand such a desire? For Witt-genstein the point would seem to be, as always, that the philosophicallogician imagines there to be a subject matter, an underlying structure,corresponding to what is necessary in the sign; on the Tractatus’ ac-count the logician imagines that in setting forth his formal languagehe has in fact laid bare that essential structure. In saying that the signsmust speak for themselves, Wittgenstein is then suggesting how mis-leading is this notion of an underlying logical structure, how an un-derstanding of logical inference is really only a matter of looking atthe symbolism in the right way.39 One is reminded here of 3.3411.After remarking that “the essential in a symbol [what is in the 6.1sreferred to as the symbol’s ‘logical properties’] is that which all sym-bols which can fulfill the same purpose have in common” (TLP 3.341),Wittgenstein, as we recall, goes on: “One could therefore say the realname is that which all symbols, which signify an object, have incommon” (TLP 3.3411). Once more it is evident that this “real name”is really no name at all:40 Wittgenstein’s account of the propositions oflogic as tautologies is meant to show that the “entity” sought by thelogician (that which is common to all the symbols) is ultimately noth-ing but a view of an entire linguistic system.The above-quoted reference to the proposition of logic as “a modus

ponens represented in signs” is meant to drive home very much thesame idea. Here Wittgenstein specifically has in mind the notion of a“rule of inference” as it functions in the formal logic of Frege andRussell. The apparent need for such inference rules can easily be takento imply that logic is concerned essentially to articulate the underlyingrelations between propositions – as if these rules provided the neces-sary justification for the transition from one proposition to another.Now earlier, at 5.132, Wittgenstein announces his rejection of anyjustificatory use of inference rules, remarking that they “are senseless(sinnlos) and would be superfluous.” His position is thus often likenedto Lewis Carroll’s in his famous article about the “paradox” surround-ing modus ponens. Carroll shows how the demand for a justificationfor the inference from “p” and “p � q” to “q” seems to require adding“(p & (p � q)) � q” as an additional premise in the inference; but bythe same reasoning, the connection between this new premise and


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the original ones would also stand in need of justification, requiring afurther premise, which then must itself be linked to the previous ones,and so on in infinite regress.41 Certainly, insofar as Wittgenstein andCarroll are both concerned to draw our attention to the special statusof rules of inference, there is a connection between their views. Butwhile Carroll’s argument may well lead us to conclude that there issome special sort of “immediate,” unformalizable character to logicalinference, the Tractatus, I suggest, is primarily concerned to shift ourperspective so that we no longer feel any urge to account for why, forexample, “q” follows from “p” and “p � q” in the first place.Wittgenstein holds that we should understand “(p & (p � q)) � q”

as a tautology; we are to see this string of signs as a sinnlos symbol thatrepresents internal features of a class of propositions, which expresseswhat is common to them. But that should make apparent that therecan be no question of justification or explanation in this context: it isnot because some given set of propositions is a tautology that we saythey have certain features in common but, rather, it is because theyshare those features that they are said to belong to the class of tautol-ogies. Since those common features are what we ordinarily refer to asinferential relations, every proposition of logic can then be said toconstitute a “modus ponens” (in an extended sense of the term) – ameans of reflecting the space of logical relations that already are takento obtain.As always, logic for Wittgenstein comes in after the fact, as it were,

as a way of describing an already given expanse of significant utter-ances. The confusion the Tractatus sees reflected in the logician’s reli-ance on inference rules betokens a reversal of this priority. The logi-cian imagines that he is in the position of legislating to language, thatthrough his rules of inference he is giving a priori license to certaininference patterns. For the Tractatus, though, what he is trying to sayhere is expressed simply in our willingness to count these particularpropositions as exemplifying a certain form, as an instance of thattautology. Rules of inference thus really constitute nothing more thana misguided attempt to specify a priori the range of certain variables –which is to say that Wittgenstein’s criticism here has much the sameform as his earlier criticism of the theory of types.42 This explains whyhe ends 6.1264 with the parenthetical remark: “And the modus po-nens [which every proposition of logic represents] cannot be ex-pressed by a proposition.” That is, Wittgenstein is suggesting that, just


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like the sort of type restrictions that Russell attempts to institute, thelogical connection between the premises “p” and “p � q” and theconclusion “q” can only be shown – everything the philosopher wouldwant to state here comes out in how we speak, in the way we operatewith a set of propositions of this form.

V

We now can begin to see how these considerations tie in with Witt-genstein’s remarks about the general form of the proposition. Thelatter notion is evidently meant to have tremendous significance inthe Tractatus: it is given extensive treatment through the 5s and indeedconstitutes the subject of one of the seven principle remarks of thebook – remark 6. We note, then, that the concept of the general formof the proposition is first introduced following the Tractatus’ initialdiscussion of tautology at 4.46–4.4661:

Now it appears to be possible to give the most general form of proposi-tion (die allgemeinste Satzform); i.e., to give a description of the proposi-tions of some one sign language, so that every possible sense can beexpressed by a symbol, which falls under the description, and so thatevery symbol which falls under the description can express a sense, ifthe meanings (Bedeutungen) of the names are chosen accordingly.It is clear that in the description of the most general form of propositiononly what is essential to it may be described – otherwise it would not bethe most general form.That there is a general form is proved by the fact that there cannot be aproposition whose form could not have been foreseen (i.e., con-structed). The general form of proposition is: Such and such is the case.(TLP 4.5)

As we have seen, the tautology (or contradiction) is for Wittgensteina means of showing what is common to certain classes of propositionsand thereby of characterizing various internal features of languageand the world. The general form of the proposition, as constitutingwhat is essential to the proposition, can then be seen as a presentationof what is common to all propositions whatsoever. It is thus a kind ofgeneralization of the tautology, giving us in the most abstract termspossible just the proposition’s way of “representing” (again in theTractarian sense of the term) the world. For this reason, Wittgenstein


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equates this general form with “the one logical constant” (TLP 5.47)and holds that its specification is “the essence of all description,therefore the essence of the world” (TLP 5.4711).Still, if it is important to see that the possibility of specifying the

general form of the proposition is continuous with the account of logicas tautologous, it is also important to be clear on how this possibilityinitially emerges out of the discussion of the picture. Once more, then,we recall that the original connection between the picture and realityis, for Wittgenstein, secured by the identity of their pictorial forms –which is to say by the fact that a picture, according to the Tractatus’way of using the term, is always a picture of the world. Given thisbackground of a common form, we can speak of all the states of affairsthat a picture can be used to depict, that is, of the existent and non-existent atomic facts that the picture “presents.” The picture is thensaid to “represent” one possibility of its projection on to those states ofaffairs and thus a kind of choice within the field of what it presents.But that means that what the picture represents – the specific deter-mination of reality that is thereby made – will always be a state ofaffairs that could obtain.43 If we can then specify in general all themethods of projecting the picture on to reality, we will have describedwhat is common to all states of affairs whatsoever – the essence of theworld. Since Wittgenstein in fact insists on the singleness of the logicalcoordinate system through which that projection occurs, the necessityof its being given all at once and in its entirety, such a complete apriori characterization of the methods of representation should thenbe available. And that is precisely what is given by his specification ofthe general form of the proposition.44

At the same time, this very story helps to make evident the empti-ness of the sort of summing up of the nature of logic allowed for bythe Tractatus. For we note at once that this a priori account of represen-tation can only be given by abstracting away from the form of thepicture, from what allows it to present the existence and nonexistenceof atomic facts. In more linguistic terms, this is just to say that theidentification of the general form of the proposition necessitates ignor-ing the specific logical forms of the propositions that are characterized.But then the expression of the general form of the proposition mustbe a (high level) variable, as 4.53 explicitly states, bringing to the forewhat is common to properties of the symbol. Thus, in 4.5, the passagequoted above, Wittgenstein says that all the symbols making up that


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expression are guaranteed to have a sense, as long as “the meaningsof the names are chosen accordingly.” Since it is only when the namesin a linguistic string actually designate meanings (i.e., logical forms)that a genuine proposition is given, this suggests that, as it stands, theexpression for the general propositional form can be no more than apossibility for a proposition, a kind of bare container in which a con-tent is to be placed.45 Wittgenstein’s paraphrase of the general form ofthe proposition as “Such and such is the case” is thus not, as Fogelinimplies,46 meant to communicate a significant result. Rather, in thetransparent vacuity of this culminating statement we are meant to seethe vacuity of the Frege/Russell logic, of any attempt to specify a priorithe limits of thought and language. Wittgenstein, in other words, ishere once more giving expression to the thought that animates thewhole Tractatus: namely, that to the extent that we can gain clarityabout the nature of our real aim in logic and philosophy, we will seethat this aim has lost its allure.47

We must be clear on how this deflationary view of the task ofphilosophy is also connected with the previously discussed notion oflogical analysis. In this regard, the above mentioned distinction be-tween “general form” and “logical form” is crucial. The logical forms,as we have seen, are equated with the meanings of the names of theelementary propositions. The possibility of giving some sort of specifi-cation of the logical forms – that is, the possibility of a completeanalysis into elementary propositions – is secured by what Wittgen-stein calls the definiteness of sense, the acknowledgment that thepossible ascriptions that may be made to reality cannot await ourdiscovery (the same thought that, as we have seen, lies behind the“argument for simples” in the opening section of the text). We sawfrom the discussion in the 3s, however, that such a specification couldonly emerge through a consideration of the proposition as it is used(of what I mean in some context) – it cannot be given in advance.This point is in fact reaffirmed several times toward the end of the 5s:

We must now answer a priori the question as to all possible forms of theelementary propositions.The elementary proposition consists of names. Since we cannot give thenumber of names with different meanings, we cannot give the compo-sition of the elementary propositions. (TLP 5.55)The enumeration of any special forms would be entirely arbitrary. (TLP5.554)


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It is clear that we have a concept of the elementary proposition apartfrom its special logical form.Where, however, we can build symbols according to a system, there thissystem is the logically important thing and not the single symbols.And how would it be possible that I should have to deal with forms inlogic which I can invent: but I must have to deal with that which makesit possible for me to invent them. (TLP 5.555)There cannot be a hierarchy of the forms of the elementary propositions.Only that which we ourselves construct can we foresee.The application (Anwendung) of logic decides what elementary proposi-tions there are.What lies in its application logic cannot anticipate. (TLP 5.557)If I cannot give elementary propositions a priori then it must lead toobvious nonsense to try to give them. (TLP 5.5571)

The actual carrying out of the analysis into elementary propositions isthus not itself part of “logic,” as Wittgenstein understands it in theTractatus. Nonetheless, the possibility of such an analysis is crucial. First,as we have seen, reflection on what it would have to entail is impor-tant in revealing the emptiness of the philosopher’s attempt to get atthe fundamental categories of thought and language – the specifica-tion of what the world, at its core, must be like. Second, the imaginedresults of this analysis figure in Wittgenstein’s summing up of thatwhich can be stated in advance – namely, the general form of theproposition. For, as we shall discuss in some detail in a moment, themore technical presentation of that general propositional form in-volves conceiving of all propositions as truth functions of the elemen-tary propositions; to be able to present the domain of the a priori in itsentirety, we must be able to conceive of the fundamental logical formsas, in some sense, given.48

One might say, then, that the notion of a complete analysis ulti-mately serves as a kind of thought experiment for gaining clarity aboutthe technical logic developed by Frege and Russell, for bringing outhow the possibility of the latter rests on our already having a handleon the meaningful content of our language. As Wittgenstein puts thepoint at 5.552: “Logic precedes every experience – that something is so.It is before the How, not before the What.” We have seen that, for theTractatus, the “what” – the content of our language – is not givenindependently of the logical scaffolding; in this sense logic precedesevery experience. But at the same time, Wittgenstein is suggesting


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that logic has no life apart from the sensical expanse with which weare presented; his real point is then that the formalisms of Frege andRussell constitute no more than an account of our way of constructingthe proposition, our manner of projecting our linguistic forms on toreality.Nonetheless, one might well wonder just how “deflationary” Witt-

genstein’s conception of this whole enterprise really is. While it maybe granted that it challenges the Frege/Russell picture of a determinatelogical content, we hardly seem to be left with nothing to replace thatpicture. On the contrary, as the above passage suggests, the Tractatuswould in the end appear to present a quite Kantian49 view of logic asa condition of the possibility of all experience. To be sure, just as withKant’s transcendental conditions of knowledge (the forms of the intu-ition and the categories of the understanding), a prior given, a “what”on which to operate, is required – thus logic can be said to determineonly “how” the world is represented. But why would that entail theemptiness of the specification of logic – that is, of the Tractarian ana-logue to Kant’s transcendental theorizing? Kant, after all, draws nosuch a conclusion about the status of his own work. Indeed, Wittgen-stein would seem to have done Kant one better, since his version oftranscendental logic is apparently capable of precise, purely formalexpression. The Tractatus’ conclusion may be a step back from themetaphysical excesses of Frege and Russell, but it ultimately does notconstitute a complete undermining of their respective enterprises.Or so one might argue. Now the general direction of (what I claim

to be) Wittgenstein’s response should, I hope, at this point be at onceapparent: his central idea is that the very possibility of formal expres-sion of the general form of the proposition itself shows the emptinessof his “transcendental philosophy.”50 Nonetheless, I do not view theabove as a mere straw man objection, as it points to the need forunderstanding in more detail Wittgenstein’s formal specification of thegeneral propositional form. How it is that [(i.e, p, , N())] is meant tosay no more than “Such and such is the case”?To answer this question, and thus to conclude this part of our

discussion of the Tractatus, we must first consider Wittgenstein’s notionof an operation. This term is introduced at 5.21: “We can bring outthese internal relations [between the structures of propositions] in ourmanner of expression, by presenting a proposition as the result of an


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operation which produced it from other propositions (the bases of theoperation).” He then continues:

The internal relation which orders a series [of forms] is equivalent tothe operation by which one term arises from another. (TLP 5.232)Truth-functions of elementary propositions are results of operationswith elementary propositions as bases. (These operations I call truth-operations.) (TLP 5.234)The sense of a truth-function of p is a function of the sense of p.Negation, logical addition, logical multiplication, etc. etc. are operations.(Negation reverses the sense of a proposition). (TLP 5.2341)

The operation is, in the first instance, Wittgenstein’s formal means ofhandling the truth functional connectives. Given our previous discus-sion of the Tractatus’ treatment of this issue, what is said here aboutthe operation should then not come as a surprise. As giving promi-nence to the representing dimension of the picture, the operation willdescribe a common feature of a class of symbols – thus Wittgensteinsays that it brings out internal relations between the structures ofpropositions. For the same reason, he remarks that “the occurrence ofan operation does not characterize the sense of a proposition” (TLP5.25): this is just to reiterate the point that the expression of a com-mon feature of a class of symbols will abstract from the logical formsof the propositions characterized, that the logical constants are onlyapplied to propositions already having a sense.51 (Wittgenstein is ofcourse not here asserting that the truth-operations have no effectwhatsoever on the sense of a proposition; after all, he expressly holdsabove that that sense is reversed by negation. Instead, what he issaying, as always in the Tractatus, is that logic assumes a pregivencontent in a certain sense, that, as an operation, it does not touch theinternal make-up of the proposition.) Similarly, too, he insists that thenotions of operation and function must not be confused with oneanother (TLP 5.25). Although both the propositional function – thatis, the symbol – and the operation – the reworking of the truth-function – are, for Wittgenstein, expressed by means of a variable (thisis explicitly stated of the operation at 5.24 and 5.2522), they stand, aswe have seen, at different levels. Hence, as 5.251 emphasizes, thefunction cannot be its own argument (“x is a table is a table” does notcharacterize any class of propositions), while the operation can takeone of its own results as its base (�p can again be denied).52


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Wittgenstein gives his more formal presentation of the notion of anoperation at 5.2522:

The general term of the formal series a, O’a, O’O’a, . . . I write thus: “[a,x, O’x].” This expression in brackets is a variable. The first term of theexpression is the beginning of the formal series, the second the form ofan arbitrary term x of the series, and the third the form of that term ofthe series which immediately follows x.

This makes it evident that, for the Tractatus, the characterization bymeans of an operation involves a recursive specification: in the varia-ble contained in the brackets, “a” represents the basis step, “x” the nthstep in the development of the series, and “O’x” (the application ofthe operation to the nth step) the nth � 1 step. To see how Wittgen-stein will make use of such a specification, we must first understandthe particular operation he is concerned to define – “N(ζ).” “,” it isclear, is a Tractarian variable, a schema for one or more propositions.As we shall soon see, however, there is a question about how exactlyto understand the functioning of the “ζ” notation. But as that questionbecomes most relevant in connection with the account of quantifica-tion, we can for the moment ignore it and simply followWittgenstein’sinstructions at 5.501 to take the “ζ” as standing for all the values of agiven variable. “N(ζ)” is then to be understood as “the negation of allthe values of the propositional variable ” (TLP 5.502); it constitutes ageneralized version of the Sheffer stroke of joint denial.Confining ourselves for the time being to the context of truth func-

tional logic, it is not difficult to see what Wittgenstein has in mind.For example, substituting “p” and “q” (which can stand for eitherelementary or nonelementary sentences) for “,” “N(p, q)” yields “�p& �q,” “N(N(p, q))” yields “�(�p & �q) & �(�p & �q),” i.e. “p v q,”and so on. The variable represented at 6-[(p, ζ, N ζ)] – then providesfor the possibility of making such selections from the set of all elemen-tary propositions. In this way, Wittgenstein can hold that he has char-acterized the whole of truth-functional logic: since the Sheffer strokeconstitutes a truth-functionally complete set, every nonquantification-ally complex sentence would appear somewhere in the formal seriesgenerated by iterated applications of the N operator to the elementarypropositions.Just this need for iterated applications of operator N is key in assess-

ing the import of this approach. For what Wittgenstein is here seeking


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to bring out is what has been implicit throughout the Tractatus –namely, that any systematic presentation of logic must rely on the“etc.,” the “and so on.”53 Indeed, he expressly remarks: “The conceptof the successive application of an operation is equivalent to the con-cept ‘and so on’ ” (TLP 5.2523).54 The point, in other words, is thatthe “givenness” of the whole of logical space – that is, of that whichthe picture was said to “present” – is ultimately just the possibility ofour always being able to go on, to continue a pattern. Certainly, ourability to identify such a pattern is important, in that it allows for thepossibility of, as Wittgenstein puts it in the Notebooks, “constructinglogic and mathematics . . . 55 from the fundamental laws and primitivesigns” (NB 89). (Conversely, we might note, precisely the absence ofthis sort of pattern precludes an a priori specification of the forms ofthe elementary propositions; one could say that there is simply noexplanation of why it is nonsense to speak of the weight of a noise.)56

But the force of Wittgenstein’s own characterization of the generalform of the proposition is to make apparent that logic is no more thanthat – that, in the end, the domain of the a priori is nothing but thepossibility57 of repeated applications of a rule.Still, even if we accept this as an interpretation of Wittgenstein’s

analysis of truth functional logic, it is not at once apparent how thissame sort of treatment could be extended to quantificational formulas.For consider how generality is expressed in the notation supplied bythe Tractatus. As that notation includes no sign for the quantifier,Wittgenstein must rely on the possibility of applying the N operator toa potentially infinite number of propositional arguments. Thus 5.52reads: “If the values of are the total values of a function fx for allvalues of x, then N() � �(∃x)fx” (TLP 5.52). In other words, if thevalues of the function “fx” are the propositions “fa,” “fb,” “fc,” . . .then “N(fx)” is equivalent to the joint denial of all those propositions,that is, to “�fa & �fb & �fc, . . . ,” an expression that is equivalent to“∀x�fx.” A further application of N would then yield the formula“∃xfx,” and so on. In this way, Wittgenstein’s N operator is capable ofhandling generality58 and in a manner that is seemingly consistentwith his truth-operational understanding of the proposition.The central question that this approach raises, however, concerns

the original specification of the values of the variable to which N isapplied.59 For what does it mean to say that a propositional variable“gives us” a set of values? If the notion of an operation is needed to


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clarify the givenness that belongs to the infinite expanse of logicalspace, how can the givenness of a potentially infinite set of proposi-tions be here treated as unproblematic? Moreover, such a view wouldcommit Wittgenstein to understanding generality in terms of logicalsum or product: to treat the variable as a name for a very lengthy listof propositional values is just to take a universally quantified state-ment as nothing but a (possibly infinitely) long conjunction. But theTractatus asserts that the concept “all” must be “disassociated from” thetruth-functions and explicitly criticizes Frege and Russell for “in-troduc[ing] generality in connexion with the logical product or thelogical sum” (TLP 5.521).One might suppose these difficulties can be circumvented by sup-

posing that, since a variable is understood as an indication of a type ofproposition, it is imagined somehow to specify its values as a set, as akind of totality. Wittgenstein’s point would then be that in denyingthis variable we simultaneously deny all its values, without having toenumerate these one by one.60 This could seem to be why he distin-guishes generality from logical sum or product. While this interpreta-tion is not altogether incorrect (as we shall see), the problem is that inrequiring that the N operator be applied directly to the propositionalvariable in this way, we run up against the earlier claim prohibitingthe operation from characterizing a sense. For N in this case effectivelyserves as a quantifier binding a free variable and thus would now beresponsible for turning an open sentence into a genuine proposition.Wittgenstein’s understanding of generality cannot then involve

such an approach. To see what he has in mind instead, we first mustlook at 5.522: “That which is peculiar to the ‘symbolism for generality’is, firstly, that it refers to a logical proto-picture (logisches Urbild;Ogden“prototype”), and secondly that it makes constants prominent.” Thisrather dark remark becomes helpful when read in connection withWittgenstein’s earlier discussion of analysis. We thus recall his discus-sion of the complex at 3.24 and its connection with the account of thevagueness of the ordinary (unanalyzed) proposition. Rather thanviewing the complex as a special kind of object on whose existencethe meaningfulness of certain propositions depends, the Tractatus, aswe saw, understands this notion linguistically – that is, as one or morelogical forms or proto-pictures that have been contracted into an ap-parent name via definition. The proto-picture here functions as ameans of leaving room for the things in the world to have a range of,


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say, color values, without our having to specify which value must beassumed. The complexity of the world is in this way reflected in acertain indeterminateness in the unanalyzed proposition. But thensince the discussion at this point is intimately connected with gener-ality (we recall 3.24’s remark – echoing 5.522 – about how the “nota-tion for generality contains a proto-picture”), it appears that it is pre-cisely through this indeterminateness that we gain our understandingof the quantifier. Generality, in other words, is to be equated with thepropositional constituent seen as a representative of an arbitrary loca-tion within a particular logical form.What this discussion first makes apparent is that generality for

Wittgenstein finds its natural home within the context of the signifi-cant (unanalyzed) proposition. After all, we saw earlier that the inde-terminateness that marks the appearance of the logical proto-pictureis understood as making possible just the definiteness of sense. In re-marking that the symbolism for generality refers to a logical proto-picture, Wittgenstein is then not faced with Russell’s problem aboutthe status of an asserted propositional function.61 He is not, in otherwords, led into viewing such a function as a genuine, self-standingproposition with a special sort of ambiguous sense. For him, instead,the application of the proto-picture is given just by its contribution tothe sense of the proposition in which it occurs; generality, we mightsay, is absorbed into our means of representing the particularities ofthe world.Still, even if Wittgenstein’s account is not saddled with the notion

of a propositional function as a self-standing assertion, one might stillwonder if his reliance on the idea of a representative of an arbitraryformal place is any clearer than Russell’s “ambiguous denoting.” Hereit becomes important to consider the above remark about the promi-nence of constants in the notation for generality. Now one mightsuppose that by “constants” Wittgenstein is thinking of “names” asopposed to “functions,” but in fact at 3.312 he uses the term in almostthe opposite sense: “[An expression] is therefore represented by thegeneral form of the propositions which it characterizes. And in thisform the expression is constant and everything else variable.” With thisin mind, his point would then seem to be that generality brings intoprominence what is common to a class of propositions, and that itdoes so precisely by taking certain parts of these propositions to be“variable,” arbitrary. For Wittgenstein, then, the possibility of speaking


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of “all” assumes not the existence of a kind of indefinite entity, but away of gesturing toward a symbol, a feature of the proposition thathelps characterize its sense. In terms of the picture theory, we couldsay that generality requires us to pay attention to the internal struc-ture of the picture – that is, to that which makes it into a picture inthe first place.62 In this way the quantifier is distinguished (“disassoci-ated”) from the truth functions, which, as we have seen, ignore thepicture’s internal makeup and concern only its projection as a whole.It is by reflection on this idea that we begin to see the key to

Wittgenstein’s view of generality: the arbitrariness that is essential toa generalization is, it seems, equivalent just to the possibility of con-structing a picture of a particular form. To illustrate, let us revert toour earlier example of the assertion “The watch is on the table.” Forthe Tractatus, both the concept “watch” and the concept “on the table”are understood as here presenting implicit generalizations, but let usfocus on the latter. How is the generality in the notion of something’sbeing on the table to be expressed? Wittgenstein would suggest that itis evident precisely in the fact that I can understand this as saying “φis at location a or φ is at b or φ is at c, and so on.” The “and so on”here does not denote the “dots of laziness”; it is not as if my sentenceconstitutes an abbreviation for a lengthy disjunction that I really in-tend. But neither does that sentence present me with a rule for contin-uing this formal series, as in the case of the truth operations. Rather,the possibility of continuing this series is given just by a logico-pictorialform. To understand the form “on the table” is to see it as permittingthis location or this location or . . . ; while I cannot list all the possiblelocations,63 still I do not happen on a place for this watch that I did notanticipate. (Recall once more Wittgenstein’s insistence that I knowwhat I mean, that I do not discover the sense of my utterances.) Thepotentially infinite set of propositional values that is “given” by aTractarian variable is here really just the possibility of placing thewatch in any location allowed for by this particular form.We now can begin to make better sense of the Tractatus’ formal way

of handling generality. This requires that we return to the difficultythat we earlier passed over – namely, the interpretation of “.” Let uslook more closely at 5.501, where the bar notation is introduced:

An expression in brackets whose terms are propositions I indicate – ifthe order of the terms in the bracket is indifferent – by a sign of the


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form “(ζ).” “” is a variable whose values are the terms of the expressionin brackets, and the line over the variable indicates that it is the repre-sentative of (vertritt) all its values in the brackets.

The problem here is that, since a variable for Wittgenstein serves tocharacterize a particular class of propositions (a point that is reiteratedat 5.501), it is not at once obvious what is the difference between “”and “.” Wouldn’t “” be “representative of all its values” – would itnot demarcate a whole class of propositions – before the bar has beenadded? We must then look at this issue in light of the above discus-sion. Given what we have seen to be Wittgenstein’s understanding ofgenerality, it would appear that what is in fact needed is to add to theexpression of a propositional variable a means of specifying somearbitrary member or members of the class of propositions that it de-scribes. This, I suggest, is precisely the function of the bar notation: toplace the bar over “” is to allow for the possibility of this variable64

standing in for65 some one or more of its values.66 Wittgenstein’s nota-tion thus bring out how the possibility of a generalization does notrequire the occurrence of a free variable, how it involves only a meansof alluding to a series of propositions of a given form.67

It now becomes clear how we are to understand the application ofthe N operator to a propositional function “fx.” By means of the barnotation we are presented with the series of “fx’s” values – “fa,” “fb,”“fc,” . . . – and it is to those values that N is directly applied. It is thentrue, as we suggested above, that the result of this operation can berepresented as “�fa & �fb & �fc,. . . .”68 This is not meant to imply,however, that the application of N requires us actually to complete a(possibly infinitely) long enumeration, as Fogelin, for example, ap-pears to hold.69 For, again, 5.521 insists that generality must not beintroduced in connection with logical sum or product; in the terms ofthe later Wittgenstein, we could say that the grammar of “infinite list”is entirely different from that of “enumeration.” For the Tractatus,then, the ellipsis here represents just our capacity to designate anyarbitrary sentence of this particular form (whatever form the variableschema “fx” is standing in for in some propositional context). Wearrive at the generalization “∀x�fx,” in other words, precisely throughthe possibility of our going on with the series “fa, fb, fc,. . . .” Given thepossibility of unlimited applications of the N operator – as well as somemeans of marking scope distinctions – we can then in the same waygenerate every sentence of first-order logic.


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The Tractatus thus can succeed in its task of showing how everyproposition is the result of truth-operations on the elementary propo-sitions. On this account, the generalization does not constitute a spe-cial kind of representation of the world, but simply a different way ofapplying a symbol. Thus, 5.526 emphasizes the potential equivalenceof a purely generalized description to description by means of names:“One can describe the world completely by completely generalizedpropositions, i.e. without from the outset co-ordinating any name witha definite object. In order then to arrive at the customary way ofexpression we need simply say after an expression “there is one andonly one x, which . . .”: and this x is a.” Rather than requiring theexistence of special sorts of general facts, the possibility of forminggeneral propositions rests once more on the possibility of continuing apattern.The notion of continuing a pattern thus plays a central, inelimin-

able role in the Tractatus’ account. This may seem unsettling: one feelsas if Wittgenstein’s specification of the general form of the propositionhas not truly gathered together, as it were, all the significant proposi-tions – that we, at best, are only shown what it would mean to makea significant utterance in some given case. But that, of course, is justthe point; that is what it is to say that we can give in advance no morethan a method for representing the world.The Tractatus’ presentation of the general propositional form tells us

that we know how to construct truth functions and sentences ofunlimited quantificational complexity. To acknowledge that as theanswer to the fundamental question of the philosophical or logicalinquiry would seem to be to acknowledge the hollowness at thatinquiry’s heart. Wittgenstein suggests that it is with this answer thatwe must rest.

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C H A P T E R I V

THE LIBERATING WORD

I

Having completed our study of the details of the Tractatus, we can nowreconsider from a more general perspective its fundamental aim oraims. There is, to be sure, a certain oddness in speaking here of a“conclusion,” given what has been maintained thus far about thenature of this text; one wonders about the status of any summaryremarks that we might have to offer. After all, if, as we have heldthroughout, a genuine understanding of the views of Wittgenstein canonly be conveyed through a detailed appreciation of the movement ofhis thought, should we not suppose that everything of importance hasalready been said? Still, the question of how the author understandsthe ultimate outcome of his endeavor remains to be directly addressed.How can it be that the Tractatus’ real purpose is an ethical one, asWittgenstein suggests?Before approaching the question, we would do well to review

where we have been. We recall, then, that this text can be understoodas, from the beginning, seeking to adopt a “logical” perspective on theworld, the perspective from which the possibility of the facts is re-vealed. This involves the attempt to specify the real nature – the form– of the objects conditioning what is the case. We saw that this form,as given by the full range of the object’s occurrences in a space ofatomic facts, cannot be conceived as a self-standing entity, let alone asa further fact about the world. Instead, it is just a particular way oflooking at what is the case: the revealing of the form of the objectturns out to involve nothing more than a description of the world thatwill make perspicuous the combinatorial capacities of that description’s


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fundamental components. While this move already shifts our under-standing of the philosophical or logical inquiry, the real force of theTractatus’ claims here only begins to become apparent in the discussionof the picture. We saw, then, how the “picture theory” reinterpretsthat inquiry’s central question as the demand for an a priori specifica-tion of the possibility of the positive/negative fact, what the Tractatuscalls the picture’s pictorial form (Form der Abbildung). The initial dis-cussion of the picture brings us to see that any insight into the possi-bility of constructing a picture that can depict the world is parasitic onan understanding of the nonarbitrary aspect of the correlation of pic-torial elements and their real-world counterparts (the analogue in thiscontext to the form of the object). That such a correlation has beeneffected is assured simply by virtue of a particular fact’s being a picture,but this possibility, according to Wittgenstein, cannot itself be repre-sented, only shown. To say that, however, is just to express the emp-tiness of the question motivating this whole inquiry; it is to suggestthat everything philosophy would want to say about the essence ofrepresentation emerges only through the application of the picture tothe world.We then saw how the treatment of picturing is extended to the

notion of the proposition via the Tractatus’ concepts of logical formand analysis. While, for Wittgenstein, the proposition is viewed ashaving a definite sense that it is the task of analysis to bring to light, itbecame apparent that this is not to be understood as an application toordinary language of a Fregean refusal to countenance vague predi-cates. Rather, the assertion of definiteness of sense is equivalent to thedenial of the possibility that I could discover what I mean, that logicalanalysis is required to reveal what my assertion really says. The ordi-nary proposition stands in perfect logical order and can do so preciselybecause it implicitly makes use of “proto-pictures” – that is, variables –that enable us to allow for a certain indeterminateness in our utter-ances. Analysis will then involve the attempt to delineate the occur-rence of those variables and thereby make perspicuous the meanings(Bedeutungen) of the names. But since for the Tractatus having a varia-ble entails already being given its (propositional) values, the variable’s“delineation” comes to no more than the specification of a particularclass of propositions. The meanings of the names emerge in what iscommon to that class – which implies that those meanings are

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not things or entities in the ordinary sense, but logical forms. Thelogical forms, in turn, are to be construed simply as ways of character-izing the already given expanse of significant utterances. What reflec-tion on the idea of analysis thus makes clear is that, just as in the caseof the picture and its form of representation, philosophy’s proper con-cern – the possibility of making sense – is not a self-subsistent domainconditioning thought and language, but just a way of viewing how wein fact speak.In Chapter III, we explored how the picture theory also underlies

Wittgenstein’s treatment of the logic of Russell’s Principia Mathematicaand Frege’s Begriffsschrift and Grundgesetze. The picture, on the onehand, “presents” (vorstellen) all those states of affairs (both existent andnonexistent) it can be used to depict. On the other hand, it “repre-sents” (darstellen) a particular state of affairs within that determinatespace; Wittgenstein thus introduces his view of the logical constants asthe specific methods by which the pictorial fact can be projected on toreality. We saw that the tautology (or contradiction) can be conceivedas a means of bringing to the fore what is common to the specificmethods of projection of a class of sentences, and hence as a way ofcharacterizing (what we would ordinarily think of as) inferential con-nections between propositions. But since, for Wittgenstein, we canspeak of what is common to any manner of representing the worldwhatsoever, it must also be possible to give the “general form” of theproposition. A kind of generalization of the tautology, this complete apriori characterization of the nature of depiction is summed up byWittgenstein’s generalized version of the Sheffer stroke, his operatorN. We saw, however, how this presentation of the general form of theproposition relies on an ineliminable use of the ellipsis and thus doesnot constitute a genuine definition. Instead, it merely points us towardthe possibility of continuing a pattern, of going on in the same way.Thus, the Tractatus’ complete a priori characterization actually bringsout the emptiness of the Fregean and Russellian view of logical infer-ence. Far from dictating to thought its fundamental laws, we aremeant to see that the formalisms of the Begriffsschrift and the Principiaserve only to reflect the hollow casing in which the significant propo-sition is to be placed.


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II

The Tractatus’ discussion of the general form of the proposition is anappropriate place to begin our final reflections on the overall purposeof Wittgenstein’s text. That discussion brings out, as we have justnoted, how the simple possibility of following a rule lies at the heartof formal logic, of our grasp of the generality of its application. Now,in the Introduction to this study and at the end of the last chapter, wesuggested that Wittgenstein’s account must itself in a certain sense relyon our ability to continue a pattern that has been initiated. After all,the Tractatus does not attempt – nor could it attempt – to unravel oneby one every confusion by which philosophy has been bedeviled.Instead, as we have emphasized, Wittgenstein seeks to carry out thistask in a wholesale manner, through a clarification of the essence ofthose confusions. This entails, ultimately, that we grasp how to extendthe kind of point the Tractatus makes to any (arbitrary) philosophical“problem” that should happen to grip us, that we are able to under-stand such a problem as a confusion, say, of formal and genuineconcepts (to use just one of the formulations Wittgenstein employs).For the Tractatus to claim to have exposed the emptiness of philosophytout court, we must be able to go on in the same way with the inquiryrepresented in the text.But now we must face up to an important dissimilarity between

the role of the “and so on” in the characterization of the significantproposition and its role in continuing the central philosophical task ofthe text as a whole. This difference is evident in the absence of anyspecification for the nonsensical pseudo-proposition corresponding tothe “general form” of the (significant) proposition – in the absence,that is, of a systematic summing-up of what is common to all thoseutterances that Wittgenstein would describe as “nonsensical.” Andindeed, on reflection we realize that it would be contrary to the Trac-tatus’ fundamental stance – its eschewal of general criteria of senseand nonsense, its reliance on a dialectical methodology – to attemptto provide any such general description of the pseudo-proposition. Toparaphrase Tolstoy, one might say that for the Tractatus all significantsentences are alike,1 while every nonsense utterance is nonsensical inits own way. There is and can be no logic of nonsense.Of course, this is largely a reformulation of the point emphasized

throughout regarding the absence of genuine arguments in the Trac-

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tatus, the inability of Wittgenstein’s text to compel us to adopt its per-spective on the nature of philosophy. But now it appears as if this ideastands in fundamental tension with the text’s aim of silencing alto-gether the philosophical voice. For without the capacity to indicatethe common component – or components – of the nonsensicalpseudo-proposition, what sense can there be in supposing that wemight continue “in the same way” Wittgenstein’s endeavor? What isthe endeavor we are to continue?One might be tempted to say that it is just on this dilemma that the

early Wittgenstein’s whole inquiry founders. But while we have em-phasized throughout how there is indeed a shift in his later thoughttoward the recognition of the multifariousness of philosophical in-quiry, it would be a mistake to suppose that Wittgenstein in theTractatus has no response whatsoever to the question we are raising.2

On the contrary, I suggest that his response is quite connected withhis understanding of the point of the text as ultimately ethical. It is inethical terms that the inquiry of the Tractatus can be said to assume aunity.We may approach this issue by first reminding ourselves of the

peculiar character of the dialectic in which this text is engaged. Overand over we have seen how Wittgenstein’s key claims – his remarksabout the nature of objects and the distinction between Tatsache andSachverhalte, the characterization of logical truths as tautologies, theshow/say distinction, and so on – can only be understood as responsesto certain philosophical questions, indeed as the means of clarifyingjust what those questions are. We have stressed how this recognitionprecludes our taking Wittgenstein’s remarks as general, self-standingclaims, how, for him, there can be no purpose, no interest whatsoeverin simply “asserting” that a logical truth is a tautology, or that certainfeatures of the proposition can only be shown. Instead, these remarksserve their clarificatory purpose – they become “nonsense” in the req-uisite sense – only when they are taken in connection with, or asdirected against, the metaphysical impulse they aim to eliminate. Theinseparability of Wittgenstein and his metaphysical interlocutor is atthe heart of the Tractarian dialectic.One then thinks back again to the Preface and Wittgenstein’s re-

mark that his book will only be understood by those who have hadthe same or similar Gedanken. We are once more reminded of 6.54 aswell, but now with a slightly different emphasis: he who understands


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me understands my propositions as nonsense. To grasp the proposi-tions of the Tractatus is, it would seem, really to engage in a doublemovement. We are to see in them the kind of thing we ourselves areaiming for and simultaneously to recognize that aim as not achievable.We are to acknowledge as illusion what we thought was our sought-after end.3 But then that is to say that the recognition of the nonsen-sicality of philosophy is, for Wittgenstein, always a recognition that weare at odds with ourselves.4 Philosophical nonsense results not becauseof anything inherently unachievable but because of an ongoing con-flict in our own desires and aims.5 The true insight into nonsense, inturn, can then be nothing but a release from self-conflict, from thisfundamental disharmony in our being. In liberating us from the innerdiscord that defines the metaphysical impulse, the Tractatus aims todeliver us to the world.We might put matters as follows. To be in the grip of philosophical

perplexity, for Wittgenstein, is not to be in a situation where one isincapable of finding a solution to a complex problem. Instead, thegenuinely philosophical “problem” only appears as such to one whoplaces certain demands on the world, on language, who insists thatour understanding must conform to this model. Wittgenstein’s aim,then, is to get us to see these demands as illegitimate, as an attempt toput our words to a task to which they are not suited; his aim is tobring us to acknowledge that our expectations for a philosophicalexplanation are in the end only our expectations. Hence his oft-quotedremark:

Most propositions and questions that have been written about philo-sophical matters are not false but nonsensical. Consequently we cannotgive any answer to questions of this kind, but can only point out thatthey are nonsensical. Most questions and propositions of philosophersarise from our failure to understand the logic of our language.(They are of the same kind as the question whether the good is more orless identical than the beautiful.)And it is not surprising that the deepest problems are in fact not prob-lems at all. (TLP 4.003)

To say that the deepest problems are not problems at all is not, how-ever, to trivialize philosophical perplexity, to sneer at those who arein its grip.6 What the above remark refers to as the depth of philosoph-ical (pseudo-) problems is taken seriously: for Wittgenstein, the im-

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pulse toward philosophy arises out of a sense of profound rupturewith the world,7 a sense that, as he puts it in the Notebooks,8 “even ifall possible scientific questions are answered our problem is still nottouched at all” (NB 51).9 Of course, this is a sense that is not peculiar tophilosophers, but, on his view, one that is apt to be experienced byanyone we should regard as serious.10 What Wittgenstein considers ascharacteristic of the philosophical approach, however, is just its ten-dency to misinterpret that feeling of disquiet, to misconstrue what isappropriate as a response. Our unease in the world crystallizes intounresolvable philosophical perplexity.This whole issue can be seen to underlie the following important

remarks:

At the basis of the whole modern view of the world lies the illusion thatthe so-called laws of nature are the explanations of natural phenomena.(TLP 6.371)So people stop short at natural laws as at something unassailable, as didthe ancients at God and Fate.And they both are right and wrong. But the ancients were clearer, in sofar as they recognized one clear terminus, whereas the modern systemmakes it appear as though everything were explained. (TLP 6.372)

Wittgenstein claims that at the basis of the modern view is an “illu-sion.” He is not suggesting, then, that the pursuit of philosophy is tobe replaced by a kind of scientism, a belief that the deepest yearningsof human beings can finally be met in the context of scientific pro-gress. But neither are we to turn to nonscientific modes of explana-tion. The ancients are here commended not for having a superiorexplanatory system, but for recognizing, in the words of the laterWittgenstein, that explanations come to an end somewhere: ratherthan serving as the basis of an ultimate “super account,” the appeal toGod or fate is, for the Tractatus, an acknowledgment that there is apoint at which nothing more can be said.Of course, it may now begin to sound as if Wittgenstein is claiming

that there are in fact genuine questions that science or human reasoncan never answer, that his philosophical task is ultimately one oflimiting reason’s scope in this regard. But we note that in the passageabove it is held that, in one respect, the moderns are right in treatingnatural laws as unassailable, as providing a complete answer. They areright because, as Wittgenstein has aimed to bring out throughout the


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Tractatus, outside of the scope of the sciences our purported explana-tions of the world are merely pseudo-accounts. For him, it is thus nota matter of placing a prohibition on reason’s ability to address certainkinds of questions, but rather of showing that those questions are notgenuine questions in the first place;11 once more the deepest problemsare held to be no problems at all. Wittgenstein’s praise of the ancients,however, connotes an attempt to caution against arriving too quicklyat this insight, against supposing too readily that our fundamentalquestions have truly dissolved. The real thrust of this passage, wemight then say, is to suggest that an easy satisfaction with the resultsof science is the wrong kind of satisfaction. We must not deceiveourselves about who we are, about what we ultimately believe. Wemust not mistake indifference or obtuseness for a genuine understand-ing of what Wittgenstein calls the “sense of life” (6.521). Instead, it isonly when we face honestly our experience of our lives as problematicthat we can hope to attain the sort of insight, the redemption that heenvisions.The Tractatus then seeks to get us to see how philosophical perplex-

ities can be expressions – indeed the complete embodiment – of thatfundamentally problematic relation to the world. Over and over, thetext attempts to expose the different guises of philosophical disquie-tude: as the demand that the picture’s fundamental relation to theworld be once and for all secured, as the need for a theory of types toprevent nonsense, as the attempt to set down a formal specification ofthe laws of thought. And over and over we are to see in responsehow, in the words of 5.473, logic must take care of itself. We are tosee, that is, how there is after all nothing for us to do to satisfy thesekinds of concerns, how it is the concerns themselves that are thesource of our fundamental unease. In gaining clarity about our philo-sophical confusions we can then be said to be liberated from theproblem of life, the sense that our fundamental relationship to theworld is something that requires a straightforward solution. ThusWitt-genstein intersperses remarks about the disappearance of philosophicalproblems with claims about the appropriate way of living in general:“The solution of the problem of life is seen in the vanishing of theproblem. (Is not this the reason why those who have found after along period of doubt that the sense of life became clear to them havethen been unable to say what constituted that sense?)” (TLP 6.521).12

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If, for the Tractatus, philosophy comes to stand for our fundamentalestrangement from the world, it is then in the disappearance of phi-losophy that our redemption lies.13

We can now return to our question of how this text’s own remarksare to be generalized to all of philosophy. The above considerationshave been intended to bring out more sharply the basis for ourfundamental contention throughout that this text’s usage of the pred-icate “nonsense” cannot be assimilated to the ordinary usage of apredicate like “red.” For while we can make straightforwardly mean-ingful judgments about the application of the latter, what we are nowseeing more clearly is that the ascription of the string “nonsense”signals, for Wittgenstein, a basic shift in our orientation toward theworld. My willingness to invoke this term carries with it the recog-nition not simply that some string of signs is illegitimate and mustbe withdrawn but, rather, that the impulse leading to the utterance ofthose signs is itself questionable.14 It is, Wittgenstein might say, myvery will that is at issue when I characterize philosophy – my ownphilosophical utterances – as nonsense.15 But that is then to suggestthat the possibility of “going on” with the Tractarian enterprise ismisdescribed when it is as presented as the problem of determiningthe future applicability of the term “nonsense.” Rather than aiming tobring me to use a word (or a whole set of words – “fact,” “thing,”“logic,” and so on) in a new manner, Wittgenstein seeks to changemy whole way of viewing, my fundamental attitude toward, phi-losophy: I am now to see the philosophical activity as essentially anattempt to make impossible demands on language and the world. Thisis not to deny that philosophical questions might arise for me after Ihave read – and understood – the Tractatus. But Wittgenstein assumesthat once we have grasped the insight at the heart of this text suchquestions will no longer tempt us. I will now see persistence in theactivity of philosophizing as an indication that my will is at odds withreality,16 that I am refusing to accept fully the course of my experi-ence.17 It will be taken as a sign that something has gone awry in myway of living. And that is to say that to “go on” with the task ofthe Tractatus is ultimately just to acknowledge the “must” in the text’sfinal remark – “Whereof one cannot speak, thereof one must remainsilent” (TLP 7) – as the mark not of logical necessity but of ethicalobligation.


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III

Wittgenstein, of course, will seemingly violate his own ethical maxim,and quite egregiously: the rest of his life is spent speaking of thosethings of which we must remain silent. This principle might thus seemto be worse than empty, for besides not even binding its own author,it serves to attach the stain of sin to philosophical inquiry. Are wenow to view philosophy as a shameful activity, my engagement in it asign of my corrupt character? Does Wittgenstein’s inability to resist itsallure not mark him as one who lacks the courage of his own convic-tions? It is tempting here to strongly resist these conclusions, to closeour study with an unequivocal endorsement of Wittgenstein’s practiceand of philosophy generally. For with regard to the former, it is un-deniably the case that Wittgenstein’s later engagement in philosophyis something other than a mere repetition of his Tractarian views;rather, as we have discussed, he is involved in deepening his originalinsight, and in so doing gives up the early governing idea of an essen-tial confusion from which we can be essentially liberated. In the Inves-tigations’ vision of philosophy, “Problems are solved (difficulties elimi-nated), not a single problem” (PI 133; emphasis Wittgenstein’s). Thereare, for the later figure, endless philosophical confusions, endlesslyvarious in their form, and hence an endless process of philosophicalclarification.18 What Wittgenstein comes to see, then, is that the wholeidea of philosophy as a “fundamental” impulse toward the world can-not be sustained.Such a shift would appear to go some way toward revoking the

Tractatus’ requirement of a kind of absolute philosophical silence; per-haps Wittgenstein may then be deemed innocent of the more seriouscharge of hypocrisy. The acceptance of this general picture seems toclear a space for our own continued involvement in philosophy aswell. For insofar as we too are forever being caught in the snare ofphilosophical perplexities, we too must continually attempt to wrigglefree from their grip – silence in this circumstance would betoken nomore than a refusal to acknowledge the reality of our own confusion.Philosophy for us thus becomes not a ladder, ascended once and thenpermanently cast aside, but a path of clarification. The Tractatus maythen be reinterpreted as the means of starting us down this route andalerting us to many of its central features.

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Still, we must temper the familiar impulse to suppose that, giventhese seemingly more modest aspirations, we are now (finally) inpossession of an entirely reliable method of philosophizing – as if, withWittgenstein, the nagging questions about the ultimate value of phil-osophical activity have once and for all been put to rest. After all,Wittgenstein’s “method,” early and late, depends always on the possi-bility of bringing us to confront the core of the “problems of philoso-phy,” with all their attendant slipperiness, their capacity to mystifyand captivate. And that is to say that his attempt to free us frommetaphysical confusion can just as easily serve to lead us more re-soundingly into its depths. Nor is this a mere idle possibility, as thedeeply metaphysical history of Tractarian scholarship might suggest.What does this mean for our understanding of the fundamental pointof the book, of the dialectical approach it exemplifies? How stable isthe state of ultimate clarity with which this text tantalizes us? If theTractatus wants us to understand philosophy as, at its heart, nothingbut illusion, it also teaches that philosophical reflection is itself ourmeans of escape. For Wittgenstein, it would seem, liberation comesonly by way of the most uncertain of paths.

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NOTES

Preface

1. See PI 97–133. An even more extended discussion of the issue is foundin the “Big Typescript,” sections 86–93 (PO 161–199).

Introduction

1. See also the occurrences of the phrase erloesende Wort at NB 39 and 54,and the use of the term erloesende and its cognates at PG 193, CV 33, andD 69, 75, 87, 99, 101.

2. I am here alluding to – and placing this book among – the cluster of“nonstandard” interpretations of the Tractatus that would include Cerbone(2000), Conant (1989, 1991, 1993, 1998, 2000), Diamond (1991a,1991b), Dreben (unpublished), Floyd (1998, in press), Goldfarb (unpub-lished), Kremer (1997), Ricketts (1996), Winch (1992), Witherspoon(2000). Friedlander (1992) might be included here as well. The clashbetween these new readings of the Tractatus and the more traditionalinterpretations, most recently defended by Hacker (2000) and Pears (un-published), forms the immediate backdrop of this study, and will bediscussed in some detail in this Introduction. McGinn (1999) discussesthis conflict and attempts to develop a kind of synthesis of the two ap-proaches; Reid (1998) offers a criticism of the Conant/Diamond positionin particular, but without completely embracing what she calls a “meta-physical” position. Biletzki (in press) also offers an overview of the de-bate, in the context of a much broader and more detailed survey ofTractarian interpretations.

3. This translation is from the original Ogden version of the Tractatus. I willgenerally rely on the Ogden version for quotations, but will occasionallytake recourse to the Pears/McGuinness translation.

4. Ramsey (1931).5. Black (1964)6. Stenius (1960).

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7. Hintikka and Hintikka (1986).8. Hacker (1986).9. Pears (1987).10. Such attempts to disregard or downplay the significance of 6.54 need not

be understood as mere oversights on the part of commentators. Instead,some justification for this strategy can be offered: one might, for example,suggest (as Pears did in a 1998 meeting of the Boston Colloquium forPhilosophy of Science) that this remark was inserted by Wittgenstein atthe close of the book simply as a means of protecting himself from criti-cism. Of course, it remains for such an interpretation to account for4.1272 at the center of the Tractatus, whose implication would seem to bemuch the same as 6.54; also, it must explain the remarks in the Notebookson pages 45 and 50, where Wittgenstein is already found to be assertingthat claims about the existence of simple objects – the sort of seeminglymeaningful claim that dominates the opening section of the Tractatus –are nonsensical. But my central point is that the invocation of suchpassages is unlikely to be conclusive; their significance too can be down-played. And that is to say that there is no easy or straightforward way tosettle this interpretive dispute.

11. See, for example, Carnap (1979) for a statement of this way of respondingto Wittgenstein’s text. We must of course bear in mind that Carnap iswriting always as a philosopher himself, and not simply as an expositorof Wittgenstein. He in fact explicitly acknowledges that his own positionmay differ from that of the Tractatus (see pp. 37–8 of Philosophy and LogicalSyntax).

12. In the language of the Tractatus, we could say that Carnap views suchformal assertions as sinnlos rather than unsinnig. Still, the real force ofcharacterizing logical proposition as tautologies is itself, like almost every-thing in the Tractatus, very delicate and open to a variety of interpreta-tions. See Dreben and Floyd (1991) for an excellent discussion of theshifting senses of the notion of tautology.

13. Anscombe (1959).14. Geach (1976).15. Hintikka and Hintikka (1986).16. Hacker espouses such a position in his classic work Insight and Illusion

(1986). He presents amore forceful argument for this view, however, in hisrecent response (2000) to Cora Diamond’s way of reading the Tractatus.

17. Diamond (1991). Warren Goldfarb (unpublished) independently arguedfor a related position in an unpublished but frequently noted 1979 paper.Dreben (unpublished), and Floyd (1998, in press) have also more or lessindependently articulated a similar interpretation of the text. As I men-tion in footnote 2, James Conant (1989, 1991, 1993, 1998, 2000) and anumber of other commentators have further elaborated the Diamondview.

18. Ramsey (1931).19. Diamond (1991, p. 185).

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20. Diamond (1991, p. 197) introduces this expression as a way of describing“a is an object,” the sort of sentence that Wittgenstein explicitly dismissesas a “nonsense pseudo-sentence” (TLP 4.1272). But clearly her contentionis that his own seemingly positive assertions have exactly the same status.

21. “Jabberwocky” is put forth by Diamond (1991, p. 96) as an example ofthe kind of thing Wittgenstein has in mind whenever he speaks of philo-sophical nonsense.

22. Diamond (1991, pp. 95–114).23. Conant (1991, pp. 341–2; 1998, pp. 244–50; 2000, pp. 194–5) tends to

emphasize this point quite strongly as well, arguing that, for Wittgenstein,philosophical nonsense resists logical segmentation and thus cannot beunderstood as resulting from the illegitimate combination of intrinsicallyintelligible components. Aside from my concerns, discussed above, aboutleaning too heavily on this particular formulation, I also worry that it canlead to attributing to Wittgenstein just the sort of theoretical doctrine thatConant most wants to avoid – as if Wittgenstein’s central aim were nowunderstood as one of giving an elaborate account of the nature of non-sense. Instead, it seems that we should say that the distinction, implicitespecially in 5.4733, between what Conant calls the “substantial” and“austere” conceptions of nonsense (2000, p. 176) belongs to the internalapparatus of the Tractatus, and as such should be seen as having the samestatus as the show/say distinction, the conception of logic as tautologous,and so forth.

24. Hacker (2000, p. 361) makes a similar point (although in a rather morecontentious manner), suggesting that Diamond surreptitiously introducesa distinction between “plain nonsense” and “transitional nonsense.”

25. See Diamond (2000).26. Conant (1991, p. 344; 1993, p. 216; 2000, p. 198) also emphasizes this

distinction.27. Diamond (2000, pp. 157–8).28. Diamond (2000, pp. 158–60).29. Reid (1998, p. 130) makes a similar point.30. Goldfarb (1997, pp. 70–2) argues in much the same way in his discussion

of Diamond’s The Realistic Spirit.31. Indeed, Hacker (2000, p. 362) tries to use something very much like this

claim as a reductio of the Conant/Diamond reading of the Tractatus.32. Goldfarb (1997) again makes something like this point with his remark

that, for Wittgenstein, “ ‘nonsense’ cannot really be a general term ofcriticism” (p. 71). Floyd (in press, p. 44) makes a similar assertion. Dia-mond, in her response to Goldfarb (1997, p. 80), appears to acknowledgethe problem, understanding it as the question of whether Wittgensteinhas “a general approach to the issue of irresoluteness.” She does not,however, attempt to provide a determinate answer.

33. Conant (1989, p. 266) presumably is saying something of this sort whenhe holds “I, over and over again, want to say something like this: ‘Wittgen-stein’s (or Kierkegaard’s) teaching cannot be stated, it can only be shown’.”

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34. In viewing this most dogmatic-seeming of texts as intrinsically dialectical,I am to some extent following Dreben (unpublished), Floyd (1998), Put-nam (1998), and Goldfarb (unpublished, 1997). Needless to say, the ideaof dialectic is rather slippery – I do not attempt to define this term – andI make no claim to be using it in exactly the same sense as any of theseauthors (indeed, it is not clear that they all understand “dialectical” injust the same way either). I think it is safe to say, however, if I may beforgiven the employment of a piece of Wittgenstein jargon, that there isat least a family resemblance amongst all these various uses of the notion.

35. See pp. 12–13.36. Again this point is essentially made in the Preface, when Wittgenstein

asserts: “In order to be able to draw a limit to thought, we should have tofind both sides of the limit thinkable (i.e., we should have to be able tothink what cannot be thought)” (TLP, p. 3).

37. The key passage from this letter reads: “The book’s point is an ethical one.I once meant to include in the preface a sentence which is not in factthere now but which I will write out for you here, because it will perhapsbe a key to the work for you. What I meant to write, then, was this: Mywork consists of two parts: the one presented here plus all I have notwritten. And it is precisely this second part that is the important one. Mybook draws limits to the sphere of the ethical from the inside as it were,and I am convinced that this is the ONLY rigorous way of drawing thoselimits” (LF 95).

38. See CV 32–3.39. Conant (1991, pp. 352–4) makes a similar point.40. Hacker (2000, pp. 371–82) emphasizes this point as part of his argument

against the Conant/Diamond reading of the Tractatus.41. See, for example, Wittgenstein’s 1931 discussion of the Tractarian under-

standing of the forms of the elementary propositions. After remarkingthat he quite rightly held in the Tractatus that those forms could not bespecified in advance, he goes on: “Yet I did think that the elementarypropositions could be specified at a later date. Only in recent years have Ibroken away from that mistake. At the time I wrote in a manuscript ofmy book (this is not printed in the Tractatus), The answers to philosophicalquestions must never be surprising. In philosophy you cannot discoveranything. I myself, however, had not clearly understood this and offendedagainst it” (VC 183). Note here how a specific alteration in one of theclaims of the Tractatus, and the seemingly theoretical description of theearlier position as a “mistake,” go along with Wittgenstein’s suggestionthat he had not truly understood the anti-theoretical character of his ownthinking. The mistake here, in other words, would not appear to consistin a false assertion in the ordinary sense but, rather, just in the impliedassimilation of philosophical claims to those claims that could be false (ortrue); such an assimilation, Wittgenstein suggests, runs counter to thespirit of the Tractatus.

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Chapter I

1. Nonetheless, many commentators have insisted on characterizing theTractatus as an essentially realist work; see, e.g., Allaire (1966, pp. 325–41), Stenius (1960), Hacker (1981, pp. 85–107), Pears (1987, p. 26),Dummet (1991). Moreover, even when such a view has been chal-lenged, it has often been by attempting to place the text into some otherstandard philosophical niche. Thus, for example, Williams (1974) arguesthat the Tractatus is in fact a (transcendental) idealist tract; while Copi(1966) and Anscombe (1959) see Wittgenstein as advocating a certainbrand of nominalism. 5.64 alone seems to suggest the hollowness of thiswhole debate.

2. See Mounce (1981, p. 19).3. Wittgenstein, in a discussion with Desmond Lee in 1930 or 1931, is in

fact explicit about the dual role of the term “logic”: “Logic may mean twothings: (1) a logical calculus as e.g. the Principia Mathematica (2) thephilosophy of logic” (CL 110).

4. Friedlander (1992, p. 83) also characterizes the role of the object in theTractatus in something like this manner, referring to the object as a “con-dition for the possibility” of the fact.

5. Cf. also 2.0131: “A spatial object must lie in infinite space. (A point inspace is an argument place). A speck in a visual field need not be red, butit must have a color; it has, so to speak, a color space round it. A tonemust have a pitch, the object of the sense of touch a hardness, etc.” Oncemore, Wittgenstein makes it clear that the object is to be identified withthe thing in its space of possibilities: it is this red speck taken togetherwith its capacity to be blue, green, yellow, etc.; this tone taken togetherwith all the other pitches it could assume; and so forth.

6. See “Function and Concept” (CP 141).7. A good deal of the literature on the Tractatus in fact involves debates over

which one of these sorts of notions Wittgenstein “really” means when hespeaks of an object.

8. In light of this point, the standard attempt to accommodate Tractarianobjects within traditional philosophical categories seems particularly mis-guided. For it is not simply that Wittgenstein suggests that, as it turns out,we cannot settle a priori whether objects are sense data, particulars, uni-versals, or what have you. Instead, part of his purpose in introducing thenotion in the way that he does is precisely to lead us away from this kindof logical categorizing. To attempt to explain the real nature of objects isto be engaged in an endeavor that is not only fruitless, but also funda-mentally obscures Wittgenstein’s real purpose.

9. See, for example, Weinberg (1966, pp. 75–85); Pears (1987, pp. 27–8, 66–72); and Fogelin (1996, pp. 14–17).

10. This will be discussed in Chapter II of this study.11. At this point, the Tractatus is clearly anticipating 3.221: “Objects I can only


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name. Signs represent them. I can only speak of them. I cannot assert them.A proposition can only say how a thing is, not what it is.”

12. Cf. NB 52: “The name of a complex functions in the proposition like thename of an object that I only know by description. – The proposition thatdepicts it functions as a description.” Cf. also this remark from two daysearlier: “ ‘Complex sign’ and ‘proposition’ are equivalent” (NB 52).

13. Friedlander (1992) makes a similar point; see pp. 84–5.14. This is the position taken by Black (1964, pp. 58–62), as well as by

Mounce (1981, pp. 19–21). I suggest that thus framing the issue in termsof a need for “immediate contact” between language and the world stemsfrom viewing Wittgenstein as ultimately resting on a Russellian notion of“knowledge by acquaintance.” But we have seen that a quite differentconception of simplicity would seem to be operating in the Tractatus.

15. Cf. TLP 5.473, which directly mirrors language from the opening remarkof the Notebooks: “Logic must take care of itself. A possible sign must alsobe able to signify.”

16. Recall from the Introduction (pp. 14–15) our contention that the wholeTractatus can be conceived as an attempt to characterize precisely thephilosophical question.

17. See, for example, Black’s introduction to the Tractatus’ discussion of thepicture: “Having concluded this account of the world as a mosaic ofatomic facts embedded in logical space, Wittgenstein now turns to con-sider what is necessarily involved in any symbolic representation of theworld. The leading question might be expressed as: Given that this iswhat the world must be, what must language be, in order to be capable ofrepresenting the world adequately? The task may be called, in Wittgen-stein’s own phraseology, that of clarifying the essence of all language,provided ‘language’ is taken to include any system of signs, not necessar-ily verbal, that is adequate for making all possible assertions about reality”(1964, p. 72).

18. Schwyzer (1966, pp. 277–8), Stripling (1978, pp. 32, 75–81), and Fried-lander (1992, p. 96) also focus on this aspect of the picture theory.

19. Here I follow Friedlander (1992) in translating vorstellen, a term thatOgden here renders as “represent,” always as “present.” This is done tomark a systematic distinction from Wittgenstein’s use of the term darstel-len, which, again like Friedlander, I translate as “represent.” The role ofdarstellen will be discussed in Chapter III.

20. Note that also mentioned here in connection with the negative fact isthe term Sachlage (translated by Ogden as “state of affairs”). The signifi-cance of this third way of speaking a fact will not be discussed untilChapter III. For the time being, it is sufficient to bear in mind that a singleSachlage appears to comprise both an existent and a nonexistent Sachver-halt.

21. See, for example, Mounce (1981, pp. 23–5).22. Black (1964, pp. 77–8).23. See, for example, Principles of Mathematics, p. 427.


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24. Recall that I always use this word as a translation of Wittgenstein’s vorstel-len.

25. The Tractatus is in this way sometimes assumed to rest on the postulationof a fundamental “isomorphism” between language and the world.Hacker (1986, p. 61) and Stenius (1960, pp. 91–6), among others, putforward this idea. Black (1964, pp. 69, 90–1) prefers the term “homomor-phism” but holds to the same basic notion of the centrality of this “hy-pothesis” to the Tractatus’ view.

26. This difficulty in assessing Wittgenstein’s real orientation toward the ques-tion at hand calls to mind his remark in Zettel 314: “Here we come upagainst a remarkable and characteristic phenomenon in philosophical in-vestigation: the difficulty – I might say – is not that of finding the solutionbut rather that of recognizing as the solution something that looks as if itwere only a preliminary to it. ‘We have already said everything. – Notanything that follows from this, no, this itself is the solution!’ This isconnected, I believe, with our wrongly expecting an explanation, whereasthe solution of the difficulty is a description, if we give it the right placein our considerations. If we dwell upon it and do not try to get beyond it.The difficulty here is: to stop.”

27. Cf. NB 108.28. This point will be key in understanding how Wittgenstein views the sense

of a proposition. For, as we shall see, it is a central tenet of the Tractatusthat the proposition’s sense – the thought that it expresses – is not givenby any external features of the propositional sign. Cf. TLP 4.002: “Lan-guage disguises the thought; so that from the external form of the clothesone cannot infer the form of the thought they clothe, because the externalform of the clothes is constructed with quite another object than to letthe form of the body be recognized.” Cf. also this remark from “Notes onLogic”: “Distrust of grammar is the first requisite for philosophizing” (NL106).

29. The same point could be made using the idea of music, the metaphor thatwe find at 4.011–4.0141. The fact that we can, for example, clap alongwith a song is in one sense arbitrary: there is no necessity that we corre-late hand claps rather than, say, the clicks of a finger with the “2” andthe “4” of each measure. But that we can represent the time in some suchway is not arbitrary – it is integral to this piece of music being the kind ofthing that it is (as is evident if we think of the ludicrousness of the attemptto clap along with a novel). Wittgenstein would then say that the possi-bility of representing the rhythm of this song by means of hand clapsultimately depends on a commonality of form.

30. He also seems to suggest this idea in NB 37.31. By contrast, the mathematical notion of an isomorphism conceives of a 1–

1 function mapping one independently given domain onto another.32. Here one begins to feel the real force of the earlier point about the

“simplicity” of objects, about how their forms only emerge through thestructure of the atomic fact.

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33. We may leave it an open question as to whether the Tractatus will ulti-mately count space as one of the logical forms – that is, as one of thefundamental categories of thought or language that will be made manifestin the elementary propositions. It is thus not yet decided whether “space”is put forward as an example of the results of logical analysis or as a mereanalogy. The issue of the relation between the notions of pictorial andlogical form and their relation to Wittgenstein’s conception of analysiswill be addressed in the next chapter.

34. See pp. 12–13.35. See also Introduction to the current study for a more general discussion

of this issue, especially of Cora Diamond’s way of criticizing the standardreading.

36. Pears (1987, p. 143).37. Here one is of course reminded of Russell’s response to the show/say

distinction in the Introduction to the Tractatus. Russell (p. 23) famouslysuggests that, while it may be impossible to express the underlying struc-ture of a language in that same language, nothing would seem to precludethe possibility of another language serving this function; such a hierarchyof languages, he holds, might indeed be infinite.

38. Pears (1987, p. 143).39. Pears (1987, p. 144).40. Note that the term abbilden is thus distinguished from vorstellen (and, as

we shall see, from darstellen as well). Whereas a picture “presents” theexistence and nonexistence of a certain set of atomic facts (and “repre-sents” a possibility of such facts), it only “depicts” reality or the world.The distinction, then, is between a picture’s relation to some specific setof facts and its fundamental role as a picture: just by virtue of being whatit is, a picture (Bild) depicts (abbildet) reality.

Chapter II

1. Pears (1987, p. 136) also raises this issue.2. See pp. 102–07 of Friedlander (1992) for his discussion of this issue.

Friedlander suggests a distinction between the pictorial form, as the con-dition of the possibility of the picture as a fact, and the logical form, as thecondition of the picture-fact’s capacity to represent some particular state ofaffairs. According to Friedlander, then, the logical form has to do withhow we use the picture as a whole to state something about the world;this notion is thus quite connected with the account of the so-calledlogical constants. Now, as will become increasingly evident, I take asextremely important this distinction between the inner composition ofthe picture and its use in representing particular states of affairs. But I donot believe that the notion of logical form is to be connected with thelatter. For, if nothing else, this assimilation would appear to fly in the faceof 2.181 (“If the pictorial form is the logical form, then the picture iscalled a logical picture.”): it does not seem to make sense to speak, even


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hypothetically, of a situation in which the pictorial form is the logicalform if these notions correspond to the very different dimensions of thepicture that Friedlander describes.

3. Here I am to some extent echoing the position of Black (1964, pp. 88–91), who distinguishes the “homologous” relation holding between thearrangement of picture elements and reality in a logical picture from the“identity” that characterizes the corresponding relation in, e.g., a spatialpicture. Unlike Black, however, I am reading Wittgenstein as ultimatelyconcerned to show that, whether we speak of a logical picture or a spatialone, the “relation” between picture elements and their real world coun-terparts is not a genuine one. Cf. also Fogelin (1976, pp. 19–20) on thisissue.

4. See Stern (1995, pp. 39–43) for a good account of Wittgenstein’s laterrejection of the picture theory, of how the notion of a picture shifts froma way of characterizing (in some sense) the proposition to a way of de-scribing the basis of the drive toward philosophical theorizing.

5. See, for example, Sellars (1966, pp. 249–51), Evans (1966, pp. 133–5),Anscombe (1959, pp. 98–101), Copi (1966, pp. 177–8), and, more re-cently, Ricketts (1996), for all of whom this remark provides evidencethat properties and relations are not Tractarian objects.

6. This was Ramsey’s (1931) view of the Tractatus’ position. From what wehave already seen about Wittgenstein’s conception of objects, such aninterpretation cannot, in general, be altogether incorrect. But in its insis-tence on relying on understanding the basic constituents of the atomicfact in terms of traditional philosophical categories, it misses what wehave suggested to be Wittgenstein’s real point about our relation to thoseforms – how it is nonsense to suppose that they could be given a priori.Moreover, as I argue immediately below, none of these issues is directlyrelevant to the real concern of 3.1432.

7. Or, we could say, it is a contingent or nonessential feature of the particu-lar pictorial method of representation used in our example that in it noproxies for spatial relations will appear.

8. In this respect, Wittgenstein’s discussion is in fact linked to Russell’s earlyworries over accounting for the peculiar unity that seems to distinguish aproposition from a mere list of its constituents (see, e.g., Principles ofMathematics, pp. 38, 51–2, 83–4).

9. The notion that, in addition to acquaintance with objects, acquaintancewith a logical form is a prerequisite for the possibility of judgment isdiscussed by Russell in Theory of Knowledge (see, e.g., pp. 99, 111), as wellas in The Philosophy of Logical Atomism. By this time, Russell no longercountenances propositions as genuine entities and thus is not concernedto account for their unity, but the problem of the unity of the judgmenthas a similar structure.

10. Frege uses this language in “Function and Concept” and “Concept and Ob-ject.” Now, of course, onemight say that Frege’s resorting tometaphor hereis an indication that, like Wittgenstein, he recognizes the impossibility

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of giving any sort of genuine account of the proposition’s unity. This, Itake it, would be part of the force of Ricketts’ insistence on the primacyof the judgment in Frege’s thought (see, e.g., Ricketts [1986]). Even so,Frege does seem to speak as if there might ultimately be a fact of thematter with regard to the question of the nature of the relation of func-tion and object, only such a fact is unavailable to us; certainly such aperception is given by Frege’s remark that the distinction between func-tions and objects is “founded on the nature of our language” (CP 194). Itis essential then to see how contrary such a position is to the Wittgenstei-nian view, as I am presenting it.

11. And here, of course, we are called back not only to 2.15, but also to 2.03:“In the atomic fact objects hang one in another, like the links of a chain.”

12. One might suppose that this remark would have served to steer commen-tators away from vain speculation about possible examples of Tractarianelementary propositions, but this has not always been the case. See, forexample, Hintikka and Hintikka’s (1986) attempt to construe such prop-ositions as statements about “immediate experience” (pp. 74–80).

13. See pp. 41 ff.14. See also TLP 5.563: “All propositions of our colloquial language are actu-

ally, just as they are, logically completely in order.”15. Here this key passage from Philosophical Grammar is especially pertinent:

“Formerly, I myself spoke of a ‘complete analysis’, and I used to believethat philosophy had to give a definitive dissection of propositions so as toset out clearly all their connections and remove all possibilities of misun-derstanding. I spoke as if there was a calculus in which such a dissectionwould be possible. I vaguely had in mind something like the definitionthat Russell had given for the definite article, and I used to think that ina similar way one would be able to use visual impressions etc. to definethe concept say of a sphere, and thus exhibit once for all the connectionsbetween the concepts and lay bare the source of all misunderstandings,etc.” (PG 211).

16. Note that in “Some Remarks on Logical Form,” it is just this sort ofprocedure that Wittgenstein describes when he offers an example of thepartial analysis of the sentence “Color patch P is red.” Thus, he imaginessetting up a coordinate system that would enable us to represent theshape and position of every patch of color in our visual system. While heoffers no sample analysis of “red” itself, he makes clear that it would betreated in the same manner – that is, by setting up a mode of representa-tion that allows for the full range of possible color ascriptions.

17. In this conception of analysis, I suggest we can see how the Tractatusmight be said to assimilate generality to logical sum or product, just asWittgenstein in Philosophical Grammar claims that it did (see PG 268 ff.).This later criticism has long puzzled commentators, since the Tractatus at5.521 apparently rebukes Frege and Russell for confusing generality withlogical sum/product. How then, Tractarian readers have wondered, canWittgenstein have been involved in the same confusion himself? The

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above discussion brings out how, in supposing that the sense of a quanti-fied statement could be captured through a specification of its instances,Wittgenstein is implicitly committed to viewing the quantifier as somehowderived from disjunction or conjunction. This in fact is precisely how hedescribes his mistake in Philosophical Grammar: “The [explanation of (∃φxas a logical sum and of (x).φx as a logical product] went with an incorrectnotion of logical analysis in that I thought that some day the logicalproduct for a particular (x).φx would be found” (PG 268). My suggestion,then, is that while the early Wittgenstein attempts to distinguish thegrammar of generality from that of the truth functions, he comes to seelater that he had not done this with sufficient sharpness.

18. Cf. Hylton’s (1997) claim: “Such a conception of sense is possible becauseWittgenstein does not accept that our thoughts are, so to speak, transpar-ent to us. He does not accept, that is to say, that if I have one thought Imust know what thought it is, that if I have two thoughts I must knowwhether they are the same, and so on” (p. 92).

19. The attraction of solipsism for Wittgenstein – part of the reason why hewill say at 5.62 that what solipsism means is quite correct – is alreadyevident in these passages. Just as he will then deflate the “truth” ofsolipsism by equating it with pure realism (see TLP 5.64), however, wemust come to see here the insubstantiality of the claim that logical anal-ysis deals only with “my” sense. The way in which such a claim might besaid to be misleading should become apparent as we go along.

20. Nonetheless, many commentators, beginning with Russell in the Intro-duction, have in fact assumed Wittgenstein’s talk of “determinateness” tosuggest that he is working within something like a Fregean framework.Thus Russell writes: “[Wittgenstein] is concerned with the conditions foraccurate Symbolism, i.e., for Symbolism in which a sentence ‘means’something quite definite. In practice, language is always more or lessvague, so that what we assert is never quite precise” (p. 8). See also Pears(1987, p. 73, n. 40).

21. See, for example, p. 68 of The Foundations of Arithmetic, where Frege as-serts that a proper definition of number must be able to tell us whetheror not Julius Caesar is a number.

22. This is stated more or less explicitly by Frege in “Function and Concept”(CP 148) and “On Sense and Reference” (CP 169), among other places.

23. Black (1964, p. 112) makes a similar point.24. Ironically, we might say that something like the same insight lies behind

Frege’s way of demanding determinateness of sense; for in requiring thatconcepts be defined for all arguments he too is acknowledging that themeaningful assertion in some sense cannot leave any possibilities open.But Frege unwittingly undermines his own insight (at least fromWittgen-stein’s point of view) by supposing that such determinacy must be some-how secured by us prior to the application of my concepts to the world.This presupposes that circumstances might arise that would lead us toshift our assessment about the meaningfulness of our assertions: for


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Frege, if my judgment contains a concept “φ” which, it turns out, fails tobe defined for some argument “a” (an argument that I may not haveanticipated when introducing the concept), I will conclude that this judg-ment, and all those containing “φ” lack a Bedeutung. But this seems toimply that it is up to the world ultimately to determine whether or notmy judgment makes sense. Frege in this way imagines a kind of divorcebetween language and its users – as if we could draw a general distinctionbetween what I think I mean by my utterance and what I in fact mean.For Wittgenstein, though, this is nothing but an admission of the intrinsicindeterminacy of sense and hence a fundamental misconstrual of the roleof logic.

25. This conception of the name is, of course, familiar from Russell’s famousdistinction between knowledge by acquaintance and knowledge by de-scription.

26. This is a conclusion reminiscent of Pears’s (1987) reading of the picturetheory. See especially pp. 142–4.

27. See Ricketts (1986, pp. 65–96).28. See VC 46.29. Here I suggest that we can see the origin of Wittgenstein’s interest in the

“seeing-as” phenomenon discussed especially in Part II of PhilosophicalInvestigations.

30. See pp. 55–6.31. Cf. this remark from the first appendix to “Notes on Logic”: “It is to be

remembered that names are not things, but classes: “A” is the same letteras “A.” This has the most important consequences for every symboliclanguage” (NB 102).

32. Principles xv.33. Black (1964), for example, appears to understand Wittgenstein’s criticisms

in this manner, suggesting that “Wittgenstein’s own programme for ‘logi-cal syntax’ can properly be viewed as an attempt to accomplish whatRussell was reaching for in his theory of types” (p. 146).

34. It is indeed just this interpretation that Carnap builds on in his The LogicalSyntax of Language.

35. Moreover, as Dreben (unpublished) has pointed out, a little reflectionwill reveal that a syntactical approach in Hilbert’s sense couldn’t satisfy theaim of Tractarian logical syntax, assuming that, as 3.324 and 3.325suggest, that aim is to rule out what Wittgenstein terms “nonsense.” Forhow would such a standard meta-mathematical approach, a specifica-tion of a formal language in terms of a set of formation rules and a setof transformation rules, preclude expressions like “The world is every-thing that is the case” or “2 � 2 is at 3 o’clock equal to 4”? It is truethat the mathematical logician will typically have no reason to include aname for “the world” or a predicate denoting “is at 3 o’clock” in hislanguage, but that is not to say that this language “rules out” expressionsformed from such notions (and, besides, if the avoidance of nonsensewere simply a matter of refraining from the use of certain terms, this

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could be accomplished in ordinary language as easily as in a formallanguage).

36. Black’s technical interpretation of the criticism, by contrast, can only bemaintained by ignoring the context of 3.331–3.333, as is evident from hischaracterization of these passages as “a digression,” albeit “a highly inter-esting one” (1964, p. 145).

37. Cf. Hintikka and Hintikka (1986) and their claim about Wittgenstein’scommitment to the “ineffability of semantics.”

38. This is, of course, not to suggest that Tractarian differences of Bedeutungwill correspond precisely to Russellian type theoretic distinctions. Russell,for example, would regard “x is brown” and “x is heavy” as belonging tothe same type of propositional function, whereas, as we have seen, Witt-genstein would distinguish them (since “the surface of the table,” e.g.,can only meaningfully be substituted in the first). The point, though, as isillustrated in this example, is that Wittgenstein’s approach is more fine-grained and will thus acknowledge at least those distinctions drawn by thetheory of types.

39. It is presumably this sort of idea that leads Wittgenstein in PhilosophicalRemarks to declare that grammar – the descendant of Tractarian logicalsyntax – “is a ‘theory of logical types’ ” (PR 7). The point here is not thatthe grammatical investigations characteristic of his later thought involveinstituting a priori restrictions on sense of the kind that we find in thetheory of types. Instead, Wittgenstein is saying that by describing clearlythe role of certain problematic expressions, “grammar” is really seekingthe same end sought by Russell – the avoidance of a certain sort ofnonsense.

40. This example is used only for the sake of illustration, since Wittgensteincomes to see that color cannot ultimately constitute one of the logicalforms. This recognition leads to the so-called color exclusion problem thatis discussed in “Some Remarks on Logical Form.”

41. See, for example, NB 20: “The internal relation between the propositionand its reference, the method of symbolizing – is the system of co-ordinates which projects the situation into the proposition. The proposi-tion corresponds to the fundamental co-ordinates.” In the persistentmetaphor of the coordinate system, we no doubt see the influence ofWittgenstein’s training as an engineer, but also, more specifically, theimportance for him of Hertz. See Grasshof (1997) for a discussion ofthe influence of Hertz, although one that draws a very different pictureof the nature of the Tractatus.

42. See Introduction to the present study.43. This would seem to be the position of Cora Diamond, who holds that, for

Wittgenstein, “the whole philosophical vocabulary reflected confusion”and hence that “we are all Benno Kerry’s through and through” (1991,p. 184).

44. Admittedly, it is not entirely clear that such objections are in the endeffectual against Frege either. After all, Frege in “Concept and Object”


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acknowledges that he is using the term “concept” in a special sense, thatis, to refer to something that is intrinsically predicative in nature. TheBegriffsschrift could then in fact be seen as helpful in clarifying what thatmeans, since it represents an example of a language in which certainkinds of signs are always used in this way. Such an interpretation ofFrege’s thought brings him closer to Wittgenstein, as Cora Diamondwould have it, since the focus here is only on characterizing a particularexpression. On the other hand, though, Frege does seem to want to claimmore than just the right to employ a term in his own peculiar sense. Foreven in “Concept and Object” he speaks of his use of the term “concept”as “purely logical” (CP 182), suggesting that it is meant to reflect thenecessary structure of our language. In this case, Frege does invite ques-tions about the status of his Begriffsschrift, of logic generally – just thekind of question that I claim the Tractatus is most concerned to get us toask.

45. Again we are called back to the opening of the Preface and the prerequi-site for understanding the book’s point that we have the same or similarthoughts as its author.

46. The notion of mathematical multiplicity also can help us make clearerWittgenstein’s claim about the uniqueness of analysis, a claim that is infact reiterated at 3.3442: “The sign of the complex is not arbitrarily re-solved in the analysis, in such a way that its resolution would be differentin every propositional structure.” To hold that there is a unique analysisof the proposition “The watch is on the table” is not to say that allacceptable analyses will literally make use of coordinate systems; such achoice is obviously arbitrary. Instead, the claim amounts to the assertionthat, whatever the specific manner of expression chosen, in every analysisthat is to count as complete the possibilities of combination of the simplesigns – the sign system’s “mathematical multiplicity” – will be the same.

47. We might, in fact, describe Wittgenstein’s later recognition of the colorexclusion problem in just these terms: as a result of reflection on whatmakes sense to say in ascriptions of color, Wittgenstein comes to see thathis so-called ab-functions – the truth tables – do not have the rightmultiplicity (at least for the task he envisioned for them) and thereforemust be either modified or rejected.

48. Such formulations, while perhaps helping to make clear why Wittgen-stein suggests that the attempt to give an a priori specification of logicalform is incoherent, appear to leave open the possibility of an a posterioricompletion of the task. Indeed, is this not what the Tractatus’ own pro-gram of analysis amounts to? This is a difficult, but quite central questionto answer if we are to understand the development of Wittgenstein’sthought. In brief, I would suggest that, in the Tractatus, he seems tosuppose that the actual carrying out of an analysis into elementary prop-ositions is no part of the task of logic (presumably just because it has anapparent a posteriori character) and that its completion would therefore beof no logico-philosophical interest (see, e.g., 5.5571). But early on in his

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“middle period” he comes to regard his Tractarian reliance on the possibil-ity of such an enterprise as illicit, as he makes clear in this remark toWaismann: “There is another mistake, which is much more dangerousand also pervades my whole book, and that is the conception that thereare questions the answers to which will be found at a later date. It is heldthat, although a result is not known, there is a way of finding it. Thus Iused to believe, for example, that it is the task of logical analysis todiscover the elementary propositions. I wrote, We are unable to specifythe form of elementary propositions, and that was quite correct too. Itwas clear to me that here at any rate there are no hypotheses and thatregarding these questions we cannot proceed by assuming from the verybeginning, as Carnap does, that the elementary propositions consist oftwo-place relations, etc. Yet I did think that the elementary propositionscould be specified at a later date. Only in recent years have I broken fromthat mistake” (VC 182). I suggest that “breaking from that mistake” comesto involve actually engaging in the analysis that is only spoken of fromafar in the Tractatus. That is, the grammatical inquiries that we find in theInvestigations are really attempts to carry out (albeit in a revised form) thepurely descriptive enterprise envisaged for Tractarian logical syntax. Thisis not to suggest that philosophy becomes for the later Wittgenstein an aposteriori discipline, but rather that he comes to see that the supposedsharp distinction between the a priori and the a posteriori must itself begiven up.

49. Cf. also 5.557: “The application of logic decides what elementary proposi-tions there are. What lies in its application logic cannot anticipate.”

50. With this understanding of the ambiguity inherent in the notion of anobject we also can make sense of the parenthetical remark at 4.123: “Hereto the shifting use of the words ‘property’ and ‘relation’ there correspondsthe shifting use of the word ‘object’.” Wittgenstein above had been com-menting on the “internal relation” of brighter and darker that obtainsbetween two different shades of blue; he then had remarked how it is“unthinkable that these two objects should not stand in this relation” (TLP4.23). It now should be evident that “object” in this context would besaid by him to designate a form, a possibility of a color, and thus, alongwith “property” and “relation” to have shifted its ordinary usage.

51. Implied here is the complete coextensiveness of “thinkability” and “logicalpossibility.” It is not, in other words, that the notion of what we can thinkserves as a criterion of what is logically possible, but rather that these twonotions are themselves internally related. We shall discuss this point ingreater detail on pp. 90–4.

52. This point will be very important both in the Tractatus’ account of tautol-ogy and in its characterization of the general form of the proposition.

53. Despite Wittgenstein’s forcefulness in this remark, some commentatorsrefuse to believe that he really intends to dismiss as incoherent theideas at the center of the philosophy of logic. Thus, for example, Black(1964) insists that the term “pseudo-concept,” which Wittgenstein uses in


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connection with “object,” “fact,” etc., “should not be read pejoratively”(p. 202), as it only serves to mark a contrast with “proper concept.” Now,it is not at once clear just why it wouldn’t be pejorative to call a concept“improper.” But presumably Black supposes that, in the manner of Car-nap (whom he quotes in this context), we can use this new distinctionbetween proper and pseudo-concepts to go on and do legitimate philo-sophical work; “pseudo-concept” constitutes, in effect, no more than atechnical term. This, however, would be anathema to Wittgenstein. In-deed, I would suggest that the full recognition of how one’s fundamentalpoint can be shifted in this way – how one’s attacks on the philosophicaltradition can be neatly turned to form a new move within that tradition –motivates in large part the style of Wittgenstein’s later writing. For hislater insistence on staying at the level of the particular case reflects pre-cisely the insight that one can always (or almost always) make sense outof a form of words, give it a new use, and hence that the Tractatus’ attemptto perform a kind of wholesale eradication of philosophical nonsense wasillegitimate.

54. We are here called back to the Introduction to this study and the discus-sion of the difficulties inherent in the endeavor to characterize the centralpoint of the Tractatus.

55. See pp. 14–15.

Chapter III

1. The heart of the later Wittgensteinian rejection of the Tractatus is, wemight say, just the recognition of such structure as illicit. For he comes tosee the notion that all the Tractarian apparatus is somehow “given” alongwith a certain view of logic as a remnant of the “a priori-ism” that he is,throughout his life, most concerned to undermine – it is at odds, then,not only with his later beliefs, but also with the very perspective that theearly text was seeking to present. Thus the later fascination with follow-ing a rule and how one step cannot be regarded as determining the next:this is just a way of tearing away the remaining shreds of any sense of anunderlying a priori structure.

2. See pp. 37 ff.3. Again I attribute this way of drawing the distinction between the Trac-

tarian terms vorstellen and darstellen to Friedlander (1992, pp. 103–07),even if his interpretation of these notions is ultimately somewhat dif-ferent from my own. I am following him in rendering the former al-ways as “present” and the latter “represent.” Few commentators havefocused on Wittgenstein’s use of these terms. Stenius (1960, pp. 98–9)notes the distinction, translating Wittgenstein’s German by different En-glish terms (vorstellen is rendered by him as “depict,” darstellen as “pres-ent”). Nonetheless, he appears to assume that these words functionmore or less as synonyms in the Tractatus; for him, the crucial distinc-


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tion is between vorstellen and abbilden. Black (1964, p. 76) explicitly as-serts that vorstellen is used by Wittgenstein “interchangeably” with dar-stellen.

4. Note that Wittgenstein does use the same term here as in the Tractatus todescribe this aspect of the picture’s relation to reality. I am not suggesting,however, that his Tractarian usage of the words darstellen and vorstellen isat this point firmly established.

5. See pp. 57–8 of this study.6. By “logical constant” I, of course, here mean “and,” “or,” “not,” and “if-

then.” Much of what Wittgenstein says about these also holds for thequantifier, but, as 5.521 makes clear, this notion is sufficiently distinct asto require separate treatment.

7. See Anscombe (1959, pp. 105–6 fn) for a discussion of this issue.8. It is interesting to compare the above Notebooks passage to the passage in

the Investigations, which also deals with this notion: “Imagine a picturerepresenting a boxer in a particular stance. Now this picture can be usedto tell someone how he should stand, should hold himself; or how heshould not hold himself; or how a particular man did stand in such-and-such a place; and so on. One might (using the language of chemistry) callthis picture a proposition-radical. This will be how Frege thought of the‘assumption’ ” (PI p. 10). Just as in 1914, Wittgenstein would appear tounderstand this Fregean notion in accordance with his own idea of thepresenting dimension of the picture.

9. This declaration in fact also appears at the very start of the Notebooks. SeeNB 2.

10. Cf. also 4.031: “In the proposition a state of affairs is, as it were, puttogether for the sake of experiment.”

11. There is then an important difference here from the situation as regardsthe elementary propositions. For, as we have seen, the notion of an apriori analysis of the elementary propositions is held to be nonsensical.(“There cannot be a hierarchy of the forms of the elementary proposi-tions. Only that which we ourselves construct can we foresee” (TLP5.556).) Central to understanding Wittgenstein’s point in presenting thegeneral form of the proposition will then be to see how he abstracts awayfrom the question of the inner constitution of the propositions he at-tempts to describe.

12. Something like this view finds expression in Pitcher (1964) and Hallet(1977), but is maintained most explicitly and extensively in Hacker(1972). See Goldfarb (unpublished) for an extremely clear and insightfulcriticism of these authors’ positions on this issue.

13. Again, Hacker (1986) explicitly puts forward this interpretation: “Theharmony between thought and reality seemed [to Wittgenstein in theTractatus] forged by psychic structures (‘the language of thought’ as somecognitive psychologists today would have it). But this, it became evident[to the later Wittgenstein], was confused on many counts. As we haveseen, expectation and its fulfillment, belief and what makes it true, desire

Notes to pp. 91–6

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and its satisfaction make contact in grammar. These internal relations arenot bound together by a shadowy mental intermediary” (p. 119).

14. Such a claim is found in many passages in Frege’s writing. One nicesummary of his standard view is found in “Logic”: “Unlike ideas, thoughtsdo not belong to the individual mind (they are not subjective), but areindependent of our thinking, and confront each one of us in the sameway (objectively). They are not the product of thinking, but are onlygrasped by thinking. In this regard they are like physical bodies. Whatdistinguishes them from physical bodies is that they are non-spatial andwe could perhaps really go as far as to say that they are essentiallytimeless – at least inasmuch as they are immune from anything that couldeffect a change in their intrinsic nature. They are like ideas in being non-spatial” (PW 148).

15. Cf. also Frege’s denials of the possibility of illogical thought at BLA 12–13and FA 20–1.

16. Hacker (1986, p. 119).17. Cf. also the end of 5.2341: “Denial reverses the sense of a proposition.”

This likewise makes it appear that the sense of a proposition is what isrepresented when that proposition is true.

18. See Chapter I, n. 20.19. McDonough (1986, pp. 26–42) introduces the term “sense1” to, in effect,

describe these “twin aspects” taken together; this is distinguished fromthe “sense2” of a proposition, which is a specification of whether theexistence of that which corresponds to the sense1 is to be “included” or“excluded” by the proposition. This is an interesting way of putting it,especially since McDonough’s sense1 would seem to correspond to whatWittgenstein, early on, in the “Notes Dictated to G. E. Moore in Norway”refers to as the “Bedeutung” of the proposition. (See NB 112: “The Bedeu-tung of a proposition is the fact that corresponds to it, e.g., if our proposi-tion be “aRb,” if it’s true, the corresponding fact would be the fact aRb, iffalse, the fact � aRb.”) Nonetheless, McDonough’s formulation is poten-tially misleading, since by dividing up the notion of sense in this way, itencourages the very sort of (Russellian) reification of facts that I claimWittgenstein is attempting to undermine. I suggest that it is to avoid sucha reification that Wittgenstein soon gives up talk of a proposition’s Bedeu-tung, and in the Tractatus expresses what he was previously reaching fornow with the notion of a picture “presenting” states of affairs. Emphasison the use of the propositional/pictorial sign, one might say, comes largelyto replace any early tendency toward the postulation of entities.

20. See Russell’s claims in Philosophy of Logical Atomism, pp. 35–47, 70–78.21. Such a view is attributed to Wittgenstein by Bradley (1992, p. 9), who

explicitly equates Wittgenstein’s position in the Tractatus with Russell’s inThe Philosophy of Logical Atomism.

22. This is what Wittgenstein means at 2.22 when he says that a picturerepresents what it represents “through the pictorial form.”

23. See, for example, Black (1964, p. 90), Bradley (1992, pp. 151–2).


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24. That, of course, simply means that the propositional constituent is herebeing used in a manner that is not consonant with its ordinary logico-syntactical employment. Thus Wittgenstein says that the sentence “Soc-rates is identical” makes no sense not because we have produced anillogical thought – we cannot go wrong at the level of the expression since,as we have seen, the expression is nothing but the sign in its significantuse – but because “we have given no meaning to the word ‘identical’ asadjective” (TLP 5.4733). It is open to us to map the use of “identical” tothat of, say, “wise,” in this context and hence give the word a meaning,but without some such measure, we must recognize we have not as yetconstructed a genuine proposition. See Diamond (1991, pp. 95–114) andConant (1991, pp. 341–2; 1998, pp. 244–50; 2000, pp. 194–5) for an elab-oration of this idea.

25. See pp. 6–7.26. Juliet Floyd (1998) puts the general point well. Noting that what the

Tractatus identifies as the unsinnig pseudo-propositions of philosophy, aswell as the sinnlos tautologies and contradictions, nearly always take theform of sentences “which obey ordinary rules of grammar” she remarks:“Wittgenstein is questioning the idea that ordinary grammar is adequateto guarantee sense” (p. 84).

27. Fogelin (1996, pp. 46–7), seeing a tension in Wittgenstein’s views, main-tains that he does not in fact ultimately deny the status of proposition-hood to the strings of logic. That is, his “theory of truth-functionality”forces him to grant that tautologies and contradictions are, in the end,legitimate combinations of signs, even if this acceptance comes with“grumbles from the side of the picture theory” expressed as 4.466’s ref-erence to these as “the disintegration of the combination of signs.”

28. Fogelin (1996, p. 82) and Black (1964, pp. 318–19), among others, as-sume such an interpretation of the Tractatus. Thus, Black maintains: “Theneed for known decision procedures for checking on putative logicaltruths is an integral and indispensable feature of Wittgenstein’s philoso-phy of logic. For he would find it intolerable that we might understand aproposition without knowing in advance how to find out whether it wasa tautology or contradiction; he could never admit that the tautologicalcharacter of a proposition might reveal itself by accident, as it were, afterwe had stumbled upon a proof of it” (p. 319).

29. Although, as Dreben and Floyd (1991, p. 32) point out, Wittgenstein doesindeed originally believe that his “ab-notation” can be extended to all oflogic and appears to arrive at his characterization of logical propositionsas tautologies with that in mind. See CL 60–1.

30. Black (1964, p. 319).31. See again Dreben and Floyd (1991) for an excellent discussion of this

whole issue.32. Bradley (1992, pp. 17–20) goes so far as to attribute this interpretation of

“tautology” to Wittgenstein himself.33. Cf. NB 109: “This is the actual procedure of [the] old Logic: it gives


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so-called primitive propositions; so-called rules of deduction; and thensays that what you get by applying the rules to the propositions is a logicalproposition that you have proved. The truth is, it tells you something aboutthe kind of proposition you have got, viz that it can be derived from thefirst symbols by these rules of combination (� is a tautology).”

34. Mounce (1981, p. 41) also makes this point.35. See again Black (1964, p. 338).36. A number of commentators have wondered at the appearance of the term

“symbol” at this point. Thus, for example, Black (1964, p. 338) com-ments: “In view of what follows immediately, one might have expectedto find ‘sign’ instead.” Brockhaus (1991, p. 204) seems to ignore thedifference between symbol and sign, even while acknowledging Wittgen-stein’s intentional use of the former term: “The occurrence of ‘symbol’ inthe first remark and ‘sign’ in the second [the second sentence of 6.126] –the emphasis, by the way, is Wittgenstein’s – implies that insofar as thesense of elementary propositions is guaranteed, we can identify tautolo-gies through purely formal rules for manipulating signs.”

37. The possibility of this sort of logical ascent with regard to the variablewould appear to have been already introduced at 3.315, where Wittgen-stein makes reference to a “nonarbitrarily determined” class of proposi-tions: “If we change a constituent part of a proposition into a variable,there is a class of propositions which are all the values of the resultingvariable proposition. This class in general depends on what, by arbitraryagreement, we mean by parts of that proposition. But if we change allthose signs, whose meaning was arbitrarily determined, into variables,there always remains such a class. But this is now no longer dependenton any agreement; it depends only on the nature of the proposition. Itcorresponds to a logical form, to a logical prototype (einem logischen Ur-bild).”

38. See, for example, Cahoone (1995, p. 198).39. Cf. 6.122 “Whence it follows that we can get on without logical proposi-

tions, for we can recognize in an adequate notation the formal propertiesof the propositions by mere inspection.”

40. This point was earlier made on p. 72.41. See Lewis Carroll (1895). Both Ricketts (1996, p. 216) and Glock (1996,

216) suggest a connection between the Carroll article and the Tractatus’view of inference rules.

42. Note that in “Notes Dictated to G. E. Moore in Norway” Wittgenstein infact immediately follows his account of logical propositions as “forms ofproof” with a discussion of the theory of types (NB, p. 109). See also TLP3.331–3.334 and our discussion on pp. 64–7.

43. In more linguistic terms, this is just to say that the application of thelogical constants will never take us beyond the domain of the (significant)proposition.

44. Cf. 5.47:


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It is clear that everything which can be said beforehand about the form ofall propositions at all can be said on one occasion.For all logical operations are already contained in the elementary propo-sition. For “fa” says the same as “(∃x).fx.x � a.”Where there is composition, there is argument and function, and wherethese are, all logical constants already are.One could say: the one logical constant is that which all propositions,according to their nature, have in common with one another.That however is the general form of proposition.

45. I owe this way of putting the matter to Juliet Floyd. Indeed, much of thissection has been inspired by her work (unpublished) on the general formof the proposition.

46. See Fogelin (1996, pp. 47–9). Fogelin acknowledges that “it is hard toread this passage without feeling let down,” that, indeed, “given theelaborate wind-up, it may even seem a joke” (p. 48). Nonetheless, hemaintains that Wittgenstein is “dead serious.” Of course, I do not denythat Wittgenstein is here serious – it is a question of what is the import ofthat seriousness.

47. Cf. also Wittgenstein’s claim at the end of the Preface: “And if I am notmistaken in this, then the value of this work secondly consists in the factthat it shows how little has been done when [the problems of philosophy]have been solved” (TLP Preface).

48. One way to understand the middle and later Wittgenstein’s shift awayfrom the perspective of the Tractatus is to see him as giving up preciselythis sharp distinction between general form and logical form, betweenwhat can be characterized in advance and what is intrinsic to the partic-ular picture/proposition as such. Wittgenstein’s dissatisfaction with theTractatus view expresses itself initially in the so-called Color ExclusionProblem discussed in “Some Remarks on Logical Form,” but perhaps moreclearly in some of his conversations with Schlick, Waismann, et al. in thelate 1920s and early 1930s. Thus, for example, in January 1930, Wittgen-stein describes his earlier conception in this way: “I laid down rules forthe syntactical use of logical constants, for example ‘p.q’, and did notthink that these rules might have something to do with the inner struc-ture of propositions. What was wrong about my conception was that Ibelieved that the syntax of logical constants could be laid down withoutpaying attention to the inner connection of propositions. That is not howthings actually are. I cannot, for example, say that red and blue are atone point simultaneously. Here no logical product can be constructed.Rather, the rules for the logical constants form only a part of a morecomprehensive syntax about which I did not yet know anything at thattime” (VC 74). Wittgenstein is not, of course, suggesting that in theTractatus he believed that one could say that red and blue are at one pointsimultaneously – this impossibility is explicitly affirmed at 6.3751: “Fortwo colours, e.g. to be at one place in the visual field is impossible,


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logically impossible, for it is excluded by the logical structure of colour.”Rather, the point is that he had thought this impossibility to be expressiblein terms of the logic capturable by his N operator and thus to require thenonelementary nature of propositions ascribing color. In coming to rec-ognize that no analysis of color propositions into logically independentelementary propositions is forthcoming, Wittgenstein is acknowledgingthe similarity of color exclusion statements (e.g., “Point A is red at time Tand point A is blue at time T”) taken as they stand to nonsensical statements– the pseudo-statements (such as “Socrates is identical”) that are, so tospeak, incompatible with the logico-pictorial forms. This then brings outthe inadequacy, the incorrect multiplicity, of the Tractatus’ specification ofthe general propositional form. At the same time, it forces a shift inWittgenstein’s conception of those unsinnig pseudo-statements – or,rather, in his conception of how one should elucidate their Unsinnigkeit.Thus he begins to focus on how the notion of logical inference is applica-ble in the case of sentences that would seem to share a logical form. Ashe puts it in his conversations with the Vienna positivists: “At that time[the time of the Tractatus] I thought that all inference was based ontautological form. At that time I had not yet seen that an inference canalso have the form: This man is 2m tall, therefore he is not 3m tall” (VC64). For Wittgenstein, this is just to suggest that, in contrast with whatthe Tractatus claims, the inner structure of the proposition, its pictorialcharacter, is describable in terms of rules – that we can to a certain extentoffer a grammar of logico-pictorial form. That insight marks the transis-tion to the far less structured, multifarious approach that characterizesWittgenstein’s work for the rest of his life.

49. The parallels between the Tractatus and Kant’s First Critique have beenoften noted. See, for example, Pears (1987, especially chapter I), Hacker(1986, pp. 22–3), Brockhaus (1991, especially chapter II), Stenius (1960,pp. 214–18), Glock (1996, p. 200), and Stern (1995, pp. 65–6, 110–13,132, 147–8).

50. Cf. the opening of the Notebooks: “Logic must take care of itself. If syntac-tical rules for functions can be set up at all (ueberhaupt), then the wholetheory of things, properties, etc. is superfluous. It is also all too obviousthat this theory isn’t what is in question either in the Grundgesetze, or inPrincipia Mathematica. Once more: logic must take care of itself” (NB 2).

51. Frascolla (1994, p. 8) misconstrues 5.25 as suggesting (in part) that “thereis no object that corresponds to an operation sign as its fixed and distin-guishable semantic value.” While the Tractatus does, of course, deny theexistence of logical objects, that is not what is at issue here. After all, to“characterize the sense of a proposition” is not to point to some thing –for then propositions would be understood as names.

52. Black (1964, p. 258) disputes Wittgenstein’s claim here, since he says thatwhat is said about operations can just as well be said of a function like“x2.” Here, however, he is simply ignoring Wittgenstein’s special use ofthe term “function.” Even Hylton’s much more careful discussion of this

Notes to p. 119

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issue in “Functions, Operations, and Sense in Wittgenstein’s Tractatus’’(1997) does not, I suggest, pay sufficient attention to the internal logic ofthe Tractatus, tying Wittgenstein’s perspective too closely to that of Fregeand Russell.

53. Juliet Floyd (unpublished) has forcefully stressed this point.54. See also Wittgenstein’s reflections in the Notebooks: “If a sentence were

ever going to be constructable it would already be constructable. Wenow need a clarification of the concept of the atomic function and theconcept ‘and so on.’ The concept ‘and so on’ symbolized by ‘ . . . ’ is oneof the most important of all and like all the others infinitely fundamen-tal. For it alone justifies us in constructing logic and mathematics ‘so on’from the fundamental laws and primitive signs. The ‘and so on’ makesits appearance right away at the very beginning of the old logic [the logicof Frege and Russell] when it is said that after the primitive signs havebeen given we can develop one sign after another ‘so on.’ Without thisconcept we should be stuck at the primitive signs and could not go‘on’ ”(NB 89–90).

55. Note that this occurrence of the ellipsis is not an instance of what Wittgen-stein is here talking about (in Tractarian terms, it signifies a differentsymbol). Rather, it constitutes an analogue to a schema for a logical form.

56. In light of this point and what was said just above in note 48 aboutWittgenstein’s development, one might suppose that his later thoughtinvolves showing, in effect, how there is an account to be given of why anoise cannot have a weight. But that is not quite accurate; Wittgenstein’slater thought is not simply a matter of showing how the Tractarian anal-ysis of the general form of the proposition can be extended to the formsof the elementary propositions. Instead, the rejection of the sharp distinc-tion between general and logico-pictorial form cuts both ways. That is,just as the notion of logical inference is brought to bear in the context ofthe inner (or, as Wittgenstein might earlier have said, “pictorial”) makeupof the proposition, so what we might call the “groundlessness” that char-acterizes the latter is seen as also applying to the former. Hence, we findthe later Wittgenstein in his discussions of rule following fundamentallyquestioning the “determinacy” that seems to belong to logic.

57. Note here how we are called back to the opening remarks of the Tractatusand the association of logic with possibility. As always, Wittgenstein willnot deny his own seemingly robustly metaphysical claims – he does notassert “p” only later to surreptitiously withdraw it – but, rather, seeks justto make manifest what, in the end, these claims come to.

58. Actually, there is, as Fogelin (1976, pp. 78–82) has pointed out, a diffi-culty in generating certain multiply quantified formulas – for example,the formula “∀x∃yFxy” – using Wittgenstein’s notation, since we are notgiven any way of making scope distinctions. Fogelin takes this to indicatea “fundamental error” in the logic of the Tractatus. It is easy enough,however, to amend the Tractarian notation so as to make it expressivelycomplete, as Geach (1981, pp. 168–71; 1982, pp. 127–8), Soames (1983,


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573–89), and Floyd (unpublished) have shown. And since, as Soamesalso points out, Wittgenstein himself at 4.0411 notes the importance of anotation’s ability to express distinctions of scope, it seems overly pedanticto find serious fault with the Tractatus for the absence of any explicitinstructions on this score.

59. At 5.523, Wittgenstein in fact would appear to suggest that our wholeunderstanding of generality turns around this initial specification: “Thegenerality symbol occurs as an argument” (TLP 5.523). The point, in otherwords, is that generality is already contained in the “x” in a propositionalvariable like “x is a table” – the quantifier does not somehow itself man-age to confer this property. It is to make this evident that Wittgenstein’snotation dispenses altogether with a sign for the quantifier.

60. Mounce (1981, pp. 65–72) argues for this view.61. See especially Principia Mathematica, pp. 38–41.62. Cf. this Notebooks assertion from 1915: “All APPEARS to be nearer the

content of the proposition than to the form. . . . Generality is essentiallyconnected with the elementary FORM. The liberating word – ?” (NB 39;caps Wittgenstein’s).

63. It is important for our understanding of Wittgenstein’s development tohere reiterate the point made last chapter (see note 17, chapter II) abouthow he comes to see himself as confused on this issue. For while theTractatus’ emphasis on the ellipsis is meant to bring out the unclarity ofthe notion of an infinite disjunction, the idea of a complete analysis seemsultimately to rest on this conception. After all, the possibility of completingthe analysis of this occurrence of “on the table” can only be realized if, inthe end, we can make a comprehensive list of spatial locations. In theTractatus, then, the dots in the above formal series must be understood asmarking only some sort of present limitation on our analytical capacities,whereas the later Wittgenstein brings out much more sharply how, forhim, it makes no sense to imagine such a possibility.

64. Or more properly, “schema for a variable,” since serves only as a place-holder for some particular propositional variable.

65. Note how the use of the term vertreten here mirrors its use at 2.31 and3.22, where, we recall, it served to describe how the pictorial/proposi-tional constituents “stand in” (or “go proxy”) for their counterparts in theworld.

66. Here I am again indebted to Juliet Floyd (unpublished), who developsthis idea in an original and very illuminating discussion of the Tractatus’treatment of “number.”

67. Cf. Wittgenstein’s 1919 letter to Russell: “I suppose you didn’t understandthe way, how I separate in the old notation of generality what is in ittruth-function and what is purely generality. A general prop[osition] is Atruth-function of all PROP[OSITION]S of a certain form” (NB 131); capsWittgenstein’s).

68. Wittgenstein also acknowledges this in the same 1919 letter to Russell


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referred to in the previous note: “You are quite right in saying ‘N()’ mayalso be made to mean �p v �q v �r v. . . . But this doesn’t matter!” (NB131).

69. See Fogelin (1976, p. 80): “The expression “(x:N(fx))” [Geach’s way ofexpressing one application of N to a function “fx”] specifies (or is short-hand for) a set of propositions that is the result of possibly infinitely many(unordered) applications of the operator N to a possibly infinite set ofpropositions.” Fogelin then goes on to argue that this requirement isinconsistent with 5.32’s assertion that all such applications must be finite.As he puts it: “If the set of base propositions is infinite, then nothingwill count as the immediate predecessor of the final application of theoperation N in the construction of a universally quantified proposition”(p. 81).

Chapter IV

1. For accuracy, we would have to add here “in a certain respect.” For thefundamental distinction we have emphasized between the general formof the proposition and the (anumerical) logical forms entails that nosystematic presentation can be given of the inner structure of the propo-sition, its internal relation to the world.

2. Besides, Wittgenstein’s later thought is not in a fundamentally differentposition with respect to the particular problem we are here addressing:we still may wonder about how that work is to be applied to philosophicalconfusions that it does not specifically treat.

3. Cf. PO 165: “Indeed we can only convict someone else of a mistake if heacknowledges that this really is the expression of his feeling. For only ifhe acknowledges it as such, is it the correct expression. (Psychoanalysis).What the other person acknowledges is the analogy I am proposing tohim as the source of his thought.”

4. Cf. CV 16: “Working in philosophy – like work in architecture in manyrespects – is really more a working on oneself. On one’s own interpreta-tion. On one’s way of seeing things. (And what one expects of them).”

5. Conant (1998; pp. 247–8) makes a similar point.6. In a similar vein, Rhees (1998, p. 40) asserts: “And that is what has to be

pressed against those who think of philosophy as therapeutic. Somethingwe have to indulge in because some people are unfortunate. You couldnever understand why Wittgenstein (and others) have wanted to com-pare philosophy with poems, in that case. The man who finds life difficult.And the man who wants to ‘put the difficulties right’.”

7. One cannot but think here of Russell’s ongoing worry about the need forimmediate contact between the mind and reality, as it is expressed inhis early rejection of idealism, in his notion of knowledge by acquain-tance, and so forth. For Wittgenstein, Russell’s attempts to “secure” thisconnection through some kind of elaborate account are paradigmatic of


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philosophical confusion. We might say that the essential thrust of theTractatus is to get us to see that such a connection can only be shown.

8. Note that the identical phrase appears at 6.52 of the Tractatus, although inan apparently different context (see the following footnote). Note alsothat in both the Tractatus and the Notebooks the quoted phrase is prefacedby the words “We feel that”; Wittgenstein is describing the sense that givesrise to philosophical perplexity, but at the same time emphasizing that itis no more than a sense, a feeling.

9. It should be noted that this Notebooks passage occurs in the context ofWittgenstein’s discussion of what he calls “the urge towards the mystical.”Given the standard interpretation of the Tractarian notion of showing asresting on the possibility of an ineffable content, the tendency amongstcommentators (Russell included) has been to understand the early Witt-genstein as in fact endorsing some version of mysticism. On this reading,it would then be mistaken to substitute, as I do, “philosophy” (whichWittgenstein is seen as wanting in some sense to counter) for “the mysti-cal” in that passage. But I would urge that Wittgenstein’s attitude towardmysticism is not univocal, that he cannot simply be described in generalas “pro” or “con.” For if we look at the whole of the remark fromNotebooks 51, it seems quite clear that in this context anyway he is decid-edly not embracing a mystical stance, at least in the sense of imagining anineffable “answer” to all outstanding nonscientific questions. The re-sponse he ultimately points to does not lie in a wordless flood of insight,but just in the recognition that “there are no questions any more.” Thatfamiliar-sounding “solution” would suggest that the mystical urge is seenas here appearing in very philosophical guise. By contrast, however, Ibelieve that we misconstrue the Tractatus’ overall aims when we seeWittgenstein, as Conant (see especially 1991) and Diamond sometimesimply, as fundamentally rejecting any notion of mysticism. While it maycertainly be granted that the text’s notion of showing does not involve agesture toward an ineffable truth (and that one way of understanding themystic would be to attribute to him the desire to make such a gesture),the reader is not thereby committed to attributing to Wittgenstein theview that “everything” must be stateable (whatever that would mean) –still less to supposing that the notion of an ineffable content is Wittgen-stein’s real target in the Tractatus.

10. Shields (1993, p. 63) makes a similar observation: “[Wittgenstein] seemsto have more respect for someone who is seriously enmeshed and both-ered by metaphysical difficulties, than for those who were never botheredat all. One gets the impression that it is somehow better to undergo aprolonged spiritual struggle in the pursuit of righteousness, than to followAristotle’s ideal and to do good spontaneously out of habit.”

11. Recall Wittgenstein’s claim in the Preface: “The book will, therefore, drawa limit to thinking, or rather – not to thinking, but to the expression ofthoughts; for, in order to draw a limit to thinking we should have to beable to think both sides of this limit (we should therefore have to be able


163

to think what cannot be thought). The limit can, therefore, only be drawnin language and what lies on the other side of the limit will be simplynonsense” (TLP p. 27). Cf. also this remark from the “Big Typescript”: “AsI have often said, philosophy does not lead me to any renunciation, sinceI do not abstain from saying something, but rather abandon a certaincombination of words as senseless. In another sense, however, philosophyrequires a resignation, but one of feeling and not of intellect. And maybethat is what makes it so difficult for many. It can be difficult not to use anexpression, just as it is difficult to hold back tears, or an outburst of anger”(PO 161).

12. One is also reminded here of this remark from Culture and Value: “Ifanyone should think he has solved the problem of life and feel like tellinghimself that everything is quite easy now, he can see that he is wrongjust by recalling that there was a time when this ‘solution’ had not beendiscovered; but it must have been possible to live then too and the solutionwhich has now been discovered seems fortuitous in relation to how thingswere then. And it is the same in the study of logic. If there were a‘solution’ to the problems of logic (philosophy) we should only need tocaution ourselves that there was a time when they had not been solved(and even at that time people must have known how to live and think)”(CV 4).

13. In this vein, it is sometimes suggested that Wittgenstein’s aim is thereforeto return us to “the ordinary”; see, e.g., Putnam’s (1993, pp. vii ff.) ac-count of what he calls the “ ‘end of philosophy’ reading of Wittgenstein”.But this is misleading. It implies that there is some special state or expe-rience that philosophers are somehow blinded to. This, for Wittgenstein,is nonsense. To posit a general notion of “ordinary experience” is toengage in just the sort of a priori categorization that the Tractatus, as wehave seen, seeks to explode. Despite the philosopher’s yearning to see hisenterprise – even in its disappearance – as aiming toward some definiteend, Wittgenstein will not allow us to say that he is returning us toanything in particular. There is simply the process of being freed fromphilosophical illusions.

14. One might then say that, in a certain sense, for Wittgenstein only I canrecognize my propositions as nonsense. That, of course, is not to denythat another might point out to me the apparent peculiarity of my utter-ances, but I alone can call them nonsense. The possibility of expressingmatters in this way can help us to see the importance of solipsism forWittgenstein, why this notion is particularly prominent in the closingpages of the book (see especially TLP 5.62–5.641). Compare this also withthe similar idea that we saw expressed in connection with the discussionof analysis, the claim that “I know what I mean” by the vague proposition(see NB 70 and pp. 212 ff. of this study).

15. Cf. this emphatic declaration at the beginning of section 86 of the “BigTypescript”: “DIFFICULTY OF PHILOSOPHY NOT THE INTELLECTUALDIFFICULTY OF THE SCIENCES, BUT THE DIFFICULTY OF A CHANGE


164

OF ATTITUDE. RESISTANCES OF THE WILL (des willens) MUST BEOVERCOME” (PO 161; caps Wittgenstein’s).

16. Or one could say, in the language of 6.373, that it is a reluctance toacknowledge the world as independent of my will.

17. By contrast, the state to which the Tractatus aims to bring us – whatWittgenstein at 6.43 calls the “world of the happy” – is characterized justby complete agreement between the self and its world. Thus, the Note-books remarks: “The happy life seems to be in some sense more harmoniousthan the unhappy” (NB 78). Of course, for Wittgenstein such harmony isnot a genuine property of an individual’s life, one element that might bepresent or absent, but rather an internal feature of his way of relating tothe world. For this reason then the Tractatus speaks of the ethical worldas “wax[ing] and wan[ing] as a whole” (TLP 6.43).

18. Still, we note that in PI 133 the original demand for “complete clarity”and the complete disappearance of philosophical problems remains.

165

BIBLIOGRAPHY

Abbreviations used:BEG BegriffsschriftBLA Basic Laws of ArithmeticCL Wittgenstein’s Lectures, Cambridge, 1930–32CP Frege’s Collected Papers on Mathematics, Logic, and PhilosophyCV Culture and ValueD Denkbewegungen: Tagebucher 1930–1932, 1936–1937FA Foundations of ArithmeticLF “Letters to Ludwig von Ficker”NB Notebooks 1914–16PG Philosophical GrammarPI Philosophical InvestigationsPO Philosophical OccasionsPR Philosophical RemarksPT PrototractatusPW Translations from the Philosophical Writings of Gottlob FregeTLP Tractatus Logico-PhilosophicusVC Ludwig Wittgenstein and the Vienna CircleZ Zettel

Allaire, E. B., 1966. “The Tractatus: Nominalistic or Realistic?,” in Essays onWittgenstein’s Tractatus, I. M. Copi and R. W. Beard (eds.). New York: Mac-millan.

Anscombe, G. E., 1959. An Introduction to Wittgenstein’s Tractatus. New York:Harper & Row.

Biletzki, A., in press. (Over)Interpreting Wittgenstein. Berkeley and Los Angeles:University of California Press.

Black, M., 1964. A Companion to Wittgenstein’s Tractatus. Ithaca, NY: CornellUniversity Press.

Bibliography

166

Bradley, R., 1992. The Nature of All Being: A Study of Wittgenstein’s Modal Atom-ism. New York: Oxford University Press.

Brockhaus, R., 1991. Pulling Up the Ladder. LaSalle, WI: Open Court.Cahoone L., 1995. The Ends of Philosophy. Albany: State University of NewYork Press.

Carnap, R., 1937. The Logical Syntax of Language. London: Routledge & KeganPaul.

———, 1979. Philosophy and Logical Syntax. New York: AMS Press.Carrol, L., 1895. “What the Tortoise Said to Achilles,” Mind n.s., IV.Cavell, S., 1979. The Claim of Reason. New York: Oxford University Press.Cerbone, D., 2000. “How to Do Things With Wood: Wittgenstein, Frege, andthe Problem of Illogical Thought,” in The New Wittgenstein, A. Crary and R.Read (eds.), pp. 292–314. London: Routledge.

Conant, J., 1989. “Must We Show What We Cannot Say,” in The Senses ofStanley Cavell, R. Fleming and M. Payne (eds.), pp. 242–83. Lewisburg, PA:Bucknell University Press.

———, 1991. “Throwing Away the Top of the Ladder.” Yale Review, vol. 79,pp. 328–64.

———, 1993. “Kierkegaard, Wittgenstein, and Nonsense,” in Pursuits of Reason,T. Cohen, P. Guyer, and H. Putnam (eds.), pp. 195–224. Lubbock: TexasTech University Press.

———, 1998. “Wittgenstein on Meaning and Use.” Philosophical Investigations,vol. 21, pp. 222–50.

———, 2000. “Elucidation and Nonsense in Frege and the Early Wittgen-stein,” in The New Wittgenstein, A. Crary and R. Read (eds.), pp. 174–217.London: Routledge.

Copi, I. M., 1966. “Objects, Properties, and Relations in the Tractatus,” in Essayson Wittgenstein’s Tractatus, I. M. Copi and R. W. Beard (eds.). New York:Macmillan.

Diamond, C., 1991. The Realistic Spirit. Cambridge, MA: MIT Press.———, 2000. “Ethics, Imagination, and the Method of Wittgenstein’s Tracta-

tus,” in The New Wittgenstein, A. Crary and R. Read (eds.), pp. 149–73.London: Routledge.

Dreben, B. Lectures, 1991–98; unpublished lecture transcriptions, 1962–98.Dreben, B. and Floyd, J., 1991. “Tautology: How Not to Use a Word.” Synthese

87, pp. 23–49.Dummett, M., 1991. The Logical Basis of Metaphysics. Cambridge, MA: HarvardUniversity Press.

Evans, E., 1966. “Tractatus 3.1432,” in Essays on Wittgenstein’s Tractatus, I. M.Copi and R. W. Beard (eds.), pp. 133–5. New York: Macmillan.

Floyd, J., 1997. Unpublished lecture.———, 1998. “The Uncaptive Eye: Solipsism in Wittgenstein’s Tractatus,” in

Loneliness, L. Rouner (ed.), pp. 79–108. Notre Dame, IN: University of NotreDame Press.

———, in press. “Number and Ascriptions of Number in Wittgenstein’s Trac-

Bibliography

167

tatus,” in From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy,E. Rech (ed.). New York: Oxford University Press.

Fogelin, R., 1976. Wittgenstein. London: Routledge & Kegan Paul.———, 1996 (2nd ed.). Wittgenstein. London: Routledge & Kegan Paul.Frascolla, P., 1994. Wittgenstein’s Philosophy of Mathematics. London: Routledge.Frege, G., 1964. Basic Laws of Arithmetic. M. Furth (ed.), M. Furth (trans.).Berkeley and Los Angeles: University of California Press.

———, 1967. Begriffsschrift, A Formula Language, Modeled Upon That of Arith-metic, For Pure Thought, in From Frege to Godel: A Source Book in MathematicalLogic, 1879–1931, J. van Heijenoort (ed.). Cambridge, MA: Harvard Univer-sity Press.

———, 1980 (3rd ed.). Translations from the Philosophical Writings of GottobFrege, M. Black and P. Geach (trans.). Oxford: Basil Blackwell.

———, 1980. The Foundations of Arithmetic, J. L. Austin (trans.). Oxford: BasilBlackwell.

———, 1984. Collected Papers on Mathematics, Logic, and Philosophy. B. Mc-Guinness (ed.), M. Black, et. al. (trans.). Oxford: Basil Blackwell.

Friedlander, E., 1992. “Expressions of Judgment,” Ph.D. Dissertation. HarvardUniversity.

Geach, P. T., 1976. “Saying and Showing in Frege and Wittgenstein,” in Essayson Wittgenstein in Honour of G. H. von Wright, J. Hintikka (ed.), Acta Philoso-phica Fennica 28. Amsterdam: North-Holland Pub. Co.

———, 1981. “Wittgenstein’s Operator N.” Analysis 41, no. 4, pp. 168–71.Glock, H., 1996. “Necessity and Normativity,” in The Cambridge Companion to

Wittgenstein, H. Sluga and D. Stern (eds.), pp. 198–225. Cambridge: Cam-bridge University Press.

Goldfarb, W., 1997. “Metaphysics and Nonsense: On Cora Diamond’s TheRealistic Spirit.” Journal of Philosophical Research 22, pp. 57–72.

———, unpublished. “Objects, Names, and Realism in the Tractatus.”Grasshof, G., 1997. “Hertzian Objects in Wittgenstein’s Tractatus.” British Jour-

nal of the History of Philosophy 5(1), pp. 87–119.Hacker, P. M. S., 1972. Insight and Illusion: Themes in the Philosophy of Wittgen-

stein. New York: Oxford University Press.———, 1986 (revised 2nd ed.). Insight and Illusion: Themes in the Philosophy of

Wittgenstein. New York: Oxford University Press.———, 2000. “Was He Trying to Whistle It?,” in The New Wittgenstein, A. Craryand R. Read (eds.), pp. 353–87. London: Routledge.

Hallet, G., 1977. A Companion to Wittgenstein’s “Philosophical Investigations.” Ith-aca, NY: Cornell University Press.

Hintikka, M. and Hintikka, J., 1986. Investigating Wittgenstein. Oxford: Black-well.

Hylton, P., 1997. “Functions, Operations, and Sense in Wittgenstein’s Tracta-tus,” in Early Analytic Philosophy, W. W. Tait (ed.), pp. 91–106. La Salle, WI:Open Court.

Kant, I., 1929. Critique of Pure Reason. N. K. Smith (trans.). London: Macmillan.

Bibliography

168

Kremer, M., 1997. “Contextualism and Holism in the Early Wittgenstein:From Prototractatus to Tractatus.” Philosophical Topics, vol. 25, pp. 87–120.

McDonough, R., 1986. The Argument of the Tractatus: Its Relevance to Contempo-rary Theories of Logic, Language, Mind, and Philosophical Truth. Buffalo: StateUniversity of New York Press.

McGinn, M., 1999. “Between Metaphysics and Nonsense: Elucidation in Witt-genstein’s Tractatus.” The Philosophical Quarterly, vol. 49, pp. 491–513.

Moore, G. E., 1901–5. “Nativism and Empiricism,” in Dictionary of Philosophyand Psychology, Baldwin, J. (ed.), vol. 2, pp. 129–32. New York: Macmillan.

Mounce, H. O., 1981. Wittgenstein’s Tractatus: An Introduction. Chicago: Univer-sity of Chicago Press.

Pears, D., 1987. The False Prison: A Study of the Development of Wittgenstein’sPhilosophy (2 vols.). Oxford: Clarendon Press.

———, unpublished. Paper delivered at the 1998 meeting of the Boston Col-loquium for Philosophy of Science.

Pitcher, G., 1964. The Philosophy of Wittgenstein. Englewood Cliffs, NJ: PrenticeHall.

Putnam, H., 1993. “Preface: Introducing Cavell,” in Pursuits of Reason, T. Co-hen, P. Guyer, and H. Putnam (eds.), pp. vii–xii. Lubbock: Texas TechUniversity Press.

———, 1998. “Floyd, Wittgenstein, and Loneliness,” in “The Uncaptive Eye:Solipsism in Wittgenstein’s Tractatus,” in Loneliness, L. Rouner (ed.),pp. 109–14. Notre Dame, IN: University of Notre Dame Press.

Ramsey, F., 1931. The Foundations of Mathematics and Other Logical Essays. Lon-don: Routledge.

Reid, L., 1998. “Wittgenstein’s Ladder: The Tractatus and Nonsense.” Philosoph-ical Investigations, vol. 21, pp. 97–151.

Rhees, R., 1997. Rush Rhees on Religion and Philosophy. D. Z. Philips (ed.).Cambridge: Cambridge University Press.

———, 1998. Wittgenstein and the Possibility of Discourse. D. Z. Philips (ed.).Cambridge: Cambridge University Press.

Ricketts, T., 1986. “Objectivity of Objecthood: Frege’s Metaphysics of Judg-ment,” in Frege Synthesized, L. Haaparanta and J. Hintikka (eds.). Dordrecht:Kluwer Academic Publishers.

———, 1996. “Pictures, Logic, and the Limits of Sense in Wittgenstein’s Trac-tatus,” in The Cambridge Companion to Wittgenstein, H. Sluga and D. G. Stern(eds.), pp. 59–99. Cambridge: Cambridge University Press.

Russell, B., 1938 (2nd ed.). Principles of Mathematics. New York: W. W. Norton.———, 1984. Theory of Knowledge The 1913 Manuscript. London: G. Allen &Unwin.

———, 1985. The Philosophy of Logical Atomism. LaSalle, WI: Open Court.Schwyzer, H. R. G., 1966. “Wittgenstein’s Picture Theory of Language,” in

Essays on Wittgenstein’s Tractatus, I. M. Copi and R. W. Beard (eds.), pp. 271–88. New York: Macmillan.

Sellars, W., 1966. “Naming and Saying,” in Essays on Wittgenstein’s Tractatus, I.Copi and R. W. Beard (eds.), pp. 249–70. New York: Macmillan.

Bibliography

169

Shields, P. R., 1993. Logic and Sin in the Writings of Ludwig Wittgenstein. Chicago:University of Chicago Press.

Soames, S., 1983. “Generality, Truth Functions, and Expressive Capacity inthe Tractatus.” Philosophical Review, XCII, No. 4, pp. 573–89.

Stenius, E., 1960. Wittgenstein’s Tractatus. Ithaca, NY: Cornell University Press.Stern, D. G., 1995. Wittgenstein on Mind and Language. New York: Oxford Uni-versity Press.

Stripling S., 1978. “The Picture Theory of Meaning: An Interpretation ofWittgenstein’s Tractatus Logico-Philosophicus,” Ph.D. Dissertation. Pennsylva-nia State University.

Weinberg, J., 1966. “Are There Ultimate Simples?,” in Essays on Wittgenstein’sTractatus, I. Copi and R. W. Beard (eds.), pp. 75–85. New York: Macmillan.

Weiner, J., 1990. Frege in Perspective. Ithaca, NY: Cornell University Press.Whitehead A. N., 1978. Process and Reality: An Essay in Cosmology. New York:Free Press.

Williams, B., 1974. “Wittgenstein and Idealism,” in Understanding Wittgenstein,G. Versey (ed.), pp. 76–95. Ithaca, NY: Cornell University Press.

Winch, P., 1992. “Persuasion,” in Midwest Studies in Philosophy, vol. 16, TheWittgenstein Legacy, P. A. French, T. E. Uehling, and H. K. Wettstein (eds.),pp. 123–37. Notre Dame, IN: University of Notre Dame Press.

Witherspoon, E., 2000. “Conceptions of Nonsense in Carnap and Wittgen-stein,” in The New Wittgenstein, A. Crary and R. Read (eds.), pp. 315–49.London: Routledge.

Wittgenstein, L., 1922. Tractatus Logico-Philosophicus. C. K. Ogden (trans.). Lon-don: Routledge & Kegan Paul.

———, 1958 (2nd ed.). Philosophical Investigations. G. E. M. Anscombe and R.Rhees (eds.), G. E. M. Anscombe (trans.), second edition. Oxford: BasilBlackwell.

———, 1967. Zettel. G. E. M. Anscombe and G. H. von Wright (eds.), G. E. M.Anscombe (trans.). Berkeley and Los Angeles: University of CaliforniaPress.

———, 1971. Prototractatus – An Early Version of Tractatus Logico-Philosophicus.B. F. McGuiness, T. Nyberg, and G. H. von Wright (eds.), D. F. Pears andB. F. McGuiness (trans.). Ithaca, NY: Cornell University Press.

———, 1974. Philosophical Grammar. R. Rhees (ed.), A. Kenny (trans.). Berke-ley and Los Angeles: University of California Press.

———, 1975. Philosophical Remarks. R. Rhees (ed.), R. Hargreaves and R.White (trans.). Chicago: University of Chicago Press.

———, 1979. “Letters to Ludwig von Ficker,” in Wittgenstein: Sources and Per-spectives, C. G. Luckhardt (ed.). Ithaca, NY: Cornell University Press.

———, 1979. Ludwig Wittgenstein and the Vienna Circle: Conversations Recorded byFriedrich Waismann. B. McGuinness (ed.), J. Schulte and B. McGuiness(trans.). Oxford: Blackwell.

———, 1979 (2nd ed.). Notebooks 1914–16. G. H. von Wright and G. E. M.Anscombe (eds.), G. E. M. Anscombe (trans.). Chicago: University of Chi-cago Press.

Bibliography

170

———, 1980 (2nd ed.). Culture and Value. G. H. Von Wright (ed.), P. Winch(trans.). Chicago: University of Chicago Press.

———, 1980. Wittgenstein’s Lectures, Cambridge, 1930–32. D. Lee (ed.). Oxford:Basil Blackwell.

———, 1993. Philosophical Occasions. J. C. Klagge and A. Nordmann (eds.).Indianapolis, IN: Hackett.

———, 1997. Denkbewegungen: Tagebucher 1930–32, 1936–37. I. Somavilla (ed.).Innsbruck: Haymon-Verlag.

171

INDEX

acquaintance, 29, 142n14, 145n9,161–2n7

analysis, 27–9, 52–9, 67–73, 98–9,114–16, 126–7, 144n33,160n63

of logical propositions, see logic,propositions of

‘‘and so on,’’ see ellipsisAnnahme, see assumptionAnscombe, G. E. M., 141n1, 145n5assumption, Fregean notion of, 83–7atomic fact [Sachverhalt], 24–5, 29,

31–4, 37, 80–1negative (nonexistent), 33–5, 37–8, 82, 94–5

see also proposition, elementaryaxiom, logical, see logical

bedeuten, see BedeutungBedeutung [meaning], 59–70, 72, 87–

8, 109, 126–7, 154n19in Frege, 91, 147–8n24

Begriffsschrift, 5–6, 9, 68, 71, 149–50n44

see also formal languageBiletzki, A., 137n2Black, M., 36, 101, 142n17, 143n25,

145n3, 148n33, 149n36, 151–2n53, 152–3n3, 155n28,156n36, 158–9n52

Bradley, R., 154n21, 155n32

Carnap, R., 4, 148n34Carrol, L., 6, 110–11categories, see logical; philosophicalcomplex, 27–30, 52–6, 76, 120

see also analysisConant, J., 5, 9–10, 139n23, 139n33,

162n9concepts, formal, 74–7pseudo-, 73, 75–6sharp boundaries of, 57see also vagueness

concept ‘‘horse’’ problem, see Fregeconcept script, see Begriffsschriftcontext principle, 60, 62contradiction, see tautologycoordinate system, 68–9, 75, 88–9,

93logical, 88–9, 93, 113

Copi, I. M., 141n1, 145n5

darstellen [represent], 80–82, 96–7,127

decision procedure, 99, 101–2, 105definition, see signs, defined; con-

cepts, sharp boundaries ofdenial, see negationdepicting relation, 40description, and the world, 23, 68,

125and structures, 28, 53, 56of expressions, 65

Index

172

dialectic, and the method of the Trac-tatus, 12–15, 43, 99, 129, 135

Diamond, C., 5–10, 139n32, 149n43,162n9

Dreben, B., 148–9n35, 155n29

element, pictorial, see pictorialellipsis, 77–8, 118–19, 122–4, 127–9,

152n1empty, see nonsenseethics, 16–17, 129–35Evans, E., 145n5expression, see symbol

fact [Tatsache], 23–4, 28, 34–6, 38–9,76–7, 95

fate, 131–2following a rule, see ellipsisFloyd, J., 155n26, 155n29, 157n45Fogelin, R., 114, 123, 155n27,

159n58, 161n69Form der Abbildung, see form, pictorialform, der Darstellung [representa-

tional], 96general, see proposition, generalform of

logical, 46–8, 50, 55–6, 63, 65–7,70–72, 78, 98–9, 114–15, 118,120–2, 127, 144n33

of objects, 25–6, 31–2, 63, 125,151n50

pictorial, 39–45, 46–8, 85, 113,126

formal language, 111, 148n35see also Begriffsschrift

formal series, 118, 122Frascolla, P., 158n51Frege, G., 36, 63–4, 91–3, 110,

147n24and analysis, 57and assumption (Annahme), 83–7,concept ‘‘horse’’ problem, 5–6, 8–9, 68–9

function/object distinction, 25–6,50–1

Friedlander, E., 47, 141n4, 142n19,152n3

function, 30, 51, 66–7, 75–7, 117,121

propositional, 61, 64–5see also Frege

Geach, P. T., 159–60n58generality, 55–6, 119–24Glock, H., 151n41God, see fateGoldfarb, W., 138n17, 139n32grammar, 143n28, 149n39Grasshof, G., 149n41Grundgedanke [fundamental

thought], of Tractatus, 86–8

Hacker, P. M. S., 94, 130n31,139n24, 143n25, 153n13

Hintikka, J. and M., 146n12Hylton, P., 147n18, 158–9n52

isomorphism, 39, 143n31

Kant, I., 39, 116

life, sense of, 132logic, 9, 23, 31, 79, 87, 99, 103, 113,

115–16and inference rules, 110–11and possibility, 22, 24, 31, 125laws of, 92–3, 127proofs in, 100–3, 105–7propositions of, see tautologytruth functional, 118–19see also philosophy

logical, atomism, 29, 95categorization, 25–27, 63, 65, 69,163n13

constants, 81–8, 127, 156n43coordinate system, see coordinatesystem, logical

inference, 34–5, 108–12inquiry, 22, 32, 44, 71–3, 79–80multiplicity, 15, 69–70, 150n46

Index

173

picture, see thoughtplace, 88space, 35, 51–2, 82–3, 88–90sum/product, 120, 123, 146–7n17

syntax, 10, 64–5, 67truth, see tautology

McDonough, R., 154n19McGinn, M., 137n2mathematical multiplicity, see logicalmeaning (see Bedeutung)metaphysics, 12–13, 15, 129–30and interpreting Tractatus, 1–2, 4,135

see also nonsense; philosophymodus ponens, logical propositions

as, 108, 110–12Mounce, H. O., 23mysticism, 162n9

N operator, 118–20, 123, 127name, 29–31, 59–60, 62–3, 67–8, 86–

7, 124, 126, 158n51apparent, 120as distinct from proposition, 36,51–3

in Frege, 91real, 72, 110

negation, 37–8, 82–3nonsense, 28, 44, 52, 67, 69–70, 74–

8, 88, 98–9, 130, 133and Carnap, see Carnapand Conant, see Conantand dialectic, 69, 99, 129and Diamond, see Diamondand showing, 4–5, 42–5Tractatus as, 2–3, 9–12, 15, 18–19,76–7, 129–30

see also metaphysics; philosophy

objects, 23–7, 33–4, 49, 51, 53, 62–4,72–3, 120, 125–6, 138n10,158n51

and atomic facts, 24–5, 31–3

and pictorial form, 39–42and substance, 30–1as formal concepts, 76–8as simple, 27–9see also analysis; Frege

operation, 116–19, 122, 124, 158n51

pattern, continuing a, see ellipsisPears, D., 43–4, 138n10philosophy, 4, 87–9, 93, 99, 102,

110, 124, 126, 133and Carnap, see Carnapand dialectic, see dialecticand nature of philosophy, ix–x,12–13, 77

and perplexity, 130–3as liberating from confusion, 1, 3,13–14, 130, 135

single problem of, 14–15, 77, 80,128–9, 134

task of, 15–16, 40, 44, 59–60, 69,71–2, 77, 79, 104, 114–15

theories in, 1, 18–19see also logic; metaphysics; non-sense

pictorial, element, 48, 50, 52, 63, 85–6, 93, 95, 126; see also form,pictorial

nature, see propositionrelationship, 39, 41

picture, 42–9, 53, 63–4, 70, 80–6, 93–7, 113, 122, 126–7

and use, 35, 37–8, 41, 48, 81–2,89, 106

as fact, 36, 50logical, see thoughtof world, 30, 99role in Tractatus, 32–3, 47see also darstellen; form, pictorial;proto-picture; vertreten; vorstel-len

possibility, see logicprojection, of the picture, 41, 43, 82,

84–5, 90, 96–7, 113and thinking 90–1, 93

Index

174

proposition, and thought, see thoughtas distinct from name, see nameas expression, see symbolas expression of its truth-conditions, 104

as measuring rod (ruler), 35, 48as picture, see picture; pictorialas setting forth possible state ofaffairs, 86

elementary, 29–30, 59–60, 70, 88,98–9, 114–15

essence of, 48, 79general form of, 79, 112–14, 116–24, 112, 127–8

indeterminateness in, 53–4, 59,121, 126, 148n24

in Frege, see Fregeof logic, see tautologypictorial nature of, 77, 87pseudo-, see nonsenseunanalyzed, 28, 53–7, 59unity of, 51, 145n8vagueness in, 57–8, 120, 163n14see also analysis; sense

propositional, function, see functionsign, see signvariable, see variable

proto-picture (prototype; Urbild), 83–4, 120–1, 126

Putnam, H., 163n13

quantifier, see generality

Ramsey, F., 5, 145n6realism, 21–2reality, 33–4, 37–8, 46, 48reference, 29–31, 36–7, 64, 91Reid, L., 137n2relations, 25, 31, 34–7, 59–60, 73, 91internal, 74, 77, 95, 117reality of, 49–51see also Bedeutung; depicting rela-tion; logical; representing rela-tion; vertreten

represent, see darstellen

representation, essence of, 40, 42,126

method of, 48, 68representing relation, 97Rhees, R., 161n6Ricketts, T., 145n5, 145–6n10,

156n41rule, following a, see ellipsisrules, inference, see logicRussell, B., 76, 110, 120–1, 144n37,

147n20, 161n7and aim of logic, 87and analysis, 27, 29, 39introduction to the Tractatus, 9,53

relations, 49–50,theory of descriptions, 54theory of types, 63–6

Sachlage, see state of affairsSachverhalt, see atomic factscience, 57–8, 131–2and logic, 22, 32, 100, 105

Sellars, W., 145n5sense, 28, 30, 38, 43, 51, 56, 61, 67–

9, 85–6, 103–05, 117, 120and Frege, 91and picture, 36, 48–50, 94–5, 97–8

bounds of, 5, 13, 17, 23definiteness of, 54, 57–9, 114,121–2, 126

lacking, see nonsense; sinnlosnot given by outer appearance ofproposition, 98–9, 143n28

see also analysis; symbolsense data, 26, 141n8senseless, see sinnlosSheffer stroke, 83, 118, 127Shields, P.R., 162n10showing, 4–5, 8, 15, 49, 70–1, 74,

161–2n7, 162n9and picture theory, 42–5, 126and tautologies, 102–04, 107–08,112

Index

175

show/say distinction, see showingsign, 11, 48–52, 58–63, 83, 99, 104,

107–08, 110, 133and theory of types, 64–7and use, 70–2, 90projection of, 88, 91, 93

silence, 13–14, 133–4simples, see objectssinnlos, 23, 97–101, 104, 107–08, 110–

11, 138n12see also nonsense; tautology

Soames, S., 159n58solipsism, 21, 147n19, 163n14space, form of, see form, pictorialstate of affairs [Sachlage], 51, 94–5,

142n20Stenius, E., 143n25, 152n3Stern, D. G., 145n4substance, see objectssymbol (expression), 60–2, 64–7, 70,

101, 104, 121–2, 159n55essential in, 72properties (features) of, 75, 106,108, 110–11, 113–14, 117

see also variablesyntax, logical, see logical

Tatsache, see facttautology, 4, 127and picture, 97–8and showing, 103–05, 107–08,112

connection with world, 109–12proof of logical proposition as, 99–102, 105–08

theory of types, see Russellthing, see objectthought (thinking), 12–13, 47, 90–4in Frege, 84, 86, 91Tractatus’ fundamental, see Gru-

ndgedanketruth, 30, 83–5, 91, 94–7

and propositions of Tractatus, 2, 4,10–12, 140n41

logical, see tautologytruth conditions, 94–5, 103truth function, 71–2 , 115, 117, 120,

122, 124, 146–7n17truth tables, 101, 103–04, 107,

150n47types, theory of, see Russell

unsinnig, see nonsense

vagueness, see propositionvariable, 55, 61–2, 66, 74–5, 111,

126and general form of proposition,113, 117–23

and tautology, 106, 108–09, 111see also symbol

vertreten [go proxy for], 36, 39–40,62–3, 86

vorstellen [present], 35–8, 81–2, 84,89, 113, 127, 114n40

Wittgenstein, L., evolution in con-ception of analysis, 140n41,146n15, 150–1n48

evolution in conception of form,47–8, 149n40, 157–8n48,159n56

evolution in conception of gener-ality, 146–7n17, 160n63

general relation between earlyand later work, 1–2, 17–19,148n29, 152n1, 153n8,164n18

history of interpreting, 3–5realization of multifariousness ofphilosophy, 129, 134–5

world, 23–4, 32–4, 38essence of, 44, 71, 113modern view of, 131–2

Wittgenstein

Documents

distinctly fregean ring

cornell university press

form der abbildung

notre dame press

harvard university press

general decision procedure

traditional philosophical categories

russells principia mathematica